關於 make a difference meaning ，我們在網路上蒐集到這些相關的討論、資訊與評價

HI HI TO ALL MY HAPPY ‘TAP” FAMILYYYY ❣️❣️❣️

I haven’t written to you all for such a long time and I do apologize so much for this. I don’t know how TIME FLIES the way it does!

I wanted to share some thoughts on this very momentous and memorable DAY in my life.. I am strolling into the BIG 6 ❤️ today!!! My BRAIN IS EMPTY!!

All I can think of is HOW GRATEFUL I am to the Universe, and to all of YOU, to my LOVING FAMILY, my INCREDIBLE FRIENDS… all this life has brought to me.. that our Planet is so beautiful and there is so much to be thankful and OPEN to.

After 60 years, chasing so many things, experiencing the excitement, ups and downs of almost all of life, months, weeks, days, minutes, seconds… and I realize, all I really desire and want, is a SIMPLE SMILE, WARMTH, UNDERSTANDING, A Heartwarming HUG, A phone call, or now, text to say HI… A Healthy and strong Body, LOTS & LOTS of LAUGHTER, CONNECTION, COMMUNICATION, LOVE, LOVE & LOVE. No matter what circumstances we run into, Rain, Thunder, Protests, Covid, it is absolutely possible to realize that ALL THINGS MUST PASS, and through the most difficult or most ravishing times, we can find comfort in holding the hands of those loving people around us. I know there is still so much more to learn while we are so BLESSED to be a VALUED GUEST on this Earth for such a fleeting moment. I feel I must keep on learning and evolving to be the BEST person I can be.

I realize that when we are born, we need so much love, feeding, nurturing, understanding, and a lot of HELP! When we get old, we need so much love, feeding, tolerance, patience, understanding, and a lot of HELP! There is no difference in the VALUE of each end of the stick. Just what we can do in between that will make ALL the difference and we all have a CHOICE in how we want to write our own, unique, wonderful, heartfelt STORY.

LIFE can be, and IS SO VERY BEAUTIFUL. The Beauty I used to understand doesn’t hold any meaning for me anymore.. The BEAUTY I HOLD TRUE is the LOVE & BEAUTY inside of ME and all the surroundings of the amazing Mother Nature. Each of us, is handcrafted so very intricately, to have all the same physical features, yet not a single one of us is a duplicate of another. We all have a brain to think, yet every single one of us does not think like any other. We ALL have a PATH, yet every one of our paths is different from each other. But we are ALL meticulously woven together, our lives, our actions are all intertwined. Every action we take, affects another. Every tree, every flower, mountain, sea, sky, clouds, animals, and all beloved creatures. We are the unique creatures, blessed with thinking, speaking & doing. I feel I must do everything I can to HONOR this special GIFT from Mother Nature. Beauty is DEEP & ROOTED & everywhere we look. I’m going to embrace everything PapaGOD & the Universe has given me.

I’m SO GRATEFUL for making it this far, in GOOD HEALTH, GOOD SPIRITS, GOOD MIND & BODY. Every day is a SURPRISE to me. Every moment is truly a BLESSING and ever so sacred. I will continue to live each BLESSED day with an open heart, open mind, and open SPIRIT. I will live each day as HIGH as I can go, no matter how low I feel. I will enjoy growing old GRACEFULLY, and make a conscious effort to do and BE the BEST I can be EACH SINGLE DAY, CHERISH & take care of it like a RARE and Beautiful JEWEL, which LIFE & our EARTH IS.

Today I spend with my LOVING FAMILY & MY FRIENDS. Well.. one loving Family is missing and in Mainland, now resting, but working VERY HARD! I’m so proud of Lam because we are so happy that he gets to SHARE his music with a WHOLE NEW GENERATION of wonderful, talented singers. It’s a GREAT BLESSING to sing with these enthusiastic Artists who can make a great difference in the world with their bellowing voices. I watch every episode with great anticipation and I hope you will too! All the Artists create their own Magic with each song & emotions!

I also would like to share with you my real and Authentic physical & Spiritual SELF!!! I just want to BE TOTALLY and ALL OF what is TRULY ME! I hope you all can accept me as I AM, white hair with my cutey wrinkles! Lam really enjoys it cos now I can keep him COMPANY & look like TWINS! I don’t know where my WHOLE self will go from here.. but I’m really going to look forward to all the natural progressions my mind and body will be taking.. just like Mother Nature.. she accepts all that comes to her and embraces it all…just as it is!

I wonder if I can remotely understand the meaning of life by now? I want to TAP (THINK ACTPOSITVE) at all times making others HAPPY & be HAPPY to see others HAPPY! I understand there is NO RIGHT or WRONG in any of our actions whether positive or negative, but only the divine consequences of those actions we choose. I feel we are BLESSED to be here with a DIVINE PURPOSE which is to help ourselves & each other. To preserve and maintain this amazing PLANET & EARTH. To evolve ourselves, & each generation, so they can pass the baton and also evolve the Earth! I also feel we are definitely NOT ALONE! NEVER! We are always in the SOOTHING, EMBRACING arms of the Divine Source Universe, and when we feel we don’t know where to turn, PapaGOD is ALWAYS there for us, ready to give us whatever we want in the deepest of our hearts with the utmost sincerity. Everything we receive is in its Divine Timing, and Divine Perfection.

With that.. HAPPYNESS & GREAT HEALTH TO ALL OF YOU FOREVER AND ALWAYS and LOVE YOURSELF as well as LOVE ALL THOSE and EVERYTHING AROUND YOU! BELIEVE ME.. ALL WE HAVE and NEED IS LOVE!!!!

MUAH MUAH MUAH with 60 YEARS OF BLESSINGS! YEHHHHHH!!!!
ALL MY LOVE!! SALLY!!!

PS. I had a great wonderful party with best of FRIENDS TONITE❣️❣️ Came home and took some selfies to shock all of U❣️❣️ My HAPPY DECADE HAPPY 6💜 GIRL (⁉️) look❣️❣️ CHEERS EVERYONE❣️❣️❣️🌹🌹🧚🏽‍♀️🧚🏽‍♀️🧚🏽‍♀️

HI HI 快樂的 “TAP” 大家庭 ❣️❣️

已經很久沒有給大家寫信了，對此我深表歉意。不知道時間怎麼就這樣過去了!

我想在生命中這個非常重要和難忘的日子和大家分享一些想法和感觸 —— 今天我悠然邁入了以6字開頭的歲月!! ❤️ 大腦一片空白!!

我所能想到的是對上天，對你們每一位，對親愛的家人，對不可思議的朋友們 —— 對生命所贈與我的這一切 —— 所懷有的深深感激。我們所生活的星球如此美麗，實在有太多太多需要去感謝、感激，去敞開心扉擁抱。

60年過去了，我也曾經追逐過很多，在每月每週每日每分每秒中，經歷了生命可能賦予的幾乎所有激動和起落，而如今我意識到，自己真正渴望和想要的，只是一個簡單的微笑，溫暖，理解，一個暖心的擁抱，一通電話，或者現在更流行的，問好的一條短信.. 一個健康強壯的身體，很多很多笑聲，連結，交流，愛，愛，以及，愛。無論我們遇到怎樣的狀況 —— 下雨、雷電、抗議、疫情，一直要謹記於心的是，無論如何，這一切終將過去；在最困難或最開心的時刻，我們都能握住身邊人的手，並從中找到最大的安慰或共鳴。能得此幸運，在如此短暫的一剎，來到地球做她的尊貴旅客，我知道還有太多東西需要學習，感覺自己必須不斷學習成長，才能成為最好的自己。

我也意識到，出生的時候，我們需要很多愛，需要被餵食物，需要關懷、滋養、理解，需要很多幫助！變老後，我們也需要很多愛，需要被餵食物，需要寬容、耐心、理解，需要很多幫助！人生兩端的價值，並沒有任何分別。只有在中間段，我們能選擇如何去書寫屬於自己的，獨特的，精彩的，發自內心的故事；而也正是在中間段所做的選擇，決定了我們會有怎樣的人生。

生活可以，也確實是非常美麗的。我曾經所理解的美，對於現時的我而言，已經沒有了當初的意義。現在，我所抱持的真正的美，是內心的愛與美，以及令人驚嘆的大自然所賦予的，環繞著我們的一切。每個人都好似複雜精緻的手工藝品，雖然有著相同的身體特徵，但沒有一個人是另一個人的複製品。我們都有大腦可以思考，但每個人和其他人想的都不同。我們都有要走的人生之路，但每個人的道路各不相同。然而，大家又被如此精心地連結在一起，彼此的生活和行為交織在一起。我們採取的每一個行動，都不可避免地影響著他人，甚至影響著每一棵樹，每一朵花；影響著山、海、天空、雲朵、動物，和所有其他可愛生靈。我們是獨一無二的存在，有福氣擁有思考、講話和行動的能力。所以我感覺自己必須盡所能去致敬和珍視這份來自自然的特殊禮物。美深深根植於我們目光所及的每處。我將擁抱上天和世界贈與我的一切。

我很感激人生走到了這裡，健康，精神，頭腦和身體都很好。每一天對我來說都是驚喜。每一刻都是充滿祝福和神聖的。我將繼續以開放的心靈、開放的思想和開放的精神去過好每一天。我會盡力去把每天過到最好，儘管有時候也會感覺低落。我將享受優雅地變老，有意識地努力在每天做到自己的最好，也成為最好的自己，珍惜和照顧匆匆而過的每日，好似它們是稀有又美麗的珠寶；而其實，生命和地球也的確如此。

今天我會和我愛的家人們和朋友們一起度過。對的，一位有愛家人不在這裡，他在內地，現在有空休息一下，但一直都在非常努力地工作! 我為Lam 感到驕傲，因為大家都非常開心他有機會同新一代如此出色、才華橫溢的年輕歌手們分享他的音樂。與這些富有激情的藝術家們一起唱歌是一種巨大的幸福；年輕一代的歌聲將給這個世界帶來改變。每一期節目我都有充滿期待地觀看，希望你們也會看！所有的藝術家們都在用每首歌和感情創造著自己的魔法！

我也想和你們分享真實的自我——外在與內在，容貌及心靈!!! 我只想做完完全全的，真正的自己！希望你們能夠接受這樣的我，白頭髮，和可愛的皺紋! Lam 很喜歡我這樣，因為現在我可以和他作伴，我們看上去像雙胞胎! 我不知道我的整個自我會從這裡走向何方，但對接下來身心將會經歷的所有自然旅程，我真心期待… 就好像大自然一樣，她接受並擁抱一切如它們本初的樣子！

我好奇自己現在是否可以算作大概開始理解人生的意義呢？我想做TAP (THINK ACTPOSITVE)，隨時通過正面積極的思考和行動為他人帶去開心，而看到他人開心也會令我感到開心！我明白我們的任何行為，無論是積極或是消極的，都無關對錯；只是，不可避免的，選擇的行為都會帶來相應的結果。我感覺帶著神聖的目的來到這裡是一份福祉，而這個目的就是助人助己，是保護和維繫這個不可思議的星球，是持續進化發展自己和每一代人，這樣他們就可以繼續把進化地球的接力棒傳遞下去! 我也感覺到我們絕對不是孤獨的！從來都不是！我們一直都被上天撫慰著，擁抱在臂膀中。當感覺不知道如何走下去，上天總會在我們身邊，以最大的誠意給予我們內心深處最渴望的所有。我們得到的一切都有它神聖的時間表，都遵循著神聖的完美安排。

以上… 祝愿大家永遠幸福開心健康，愛自己，愛周圍的所有人，愛周圍的一切！相信我… 我們所擁有的和需要的一切，就是愛!!!!

MUAH MUAH MUAH with 60 YEARS OF BLESSINGS! YEHHHHH!!!!
ALL MY LOVE!! SALLY!!!

PS. 今晚我和最好的朋友們開了最棒的Party ❣️❣️❣️ 回到家後拍了幾張自拍，肯定會驚到你們 ❣️❣️❣️ 我的快樂第6個10年 💜 GIRL (⁉️) look❣️❣️❣️ 大家乾杯 ❣️❣️❣️🌹🌹🧚🏻‍♀️🧚🏻‍♀️🧚🏻‍♀️

CAPTION TIẾNG ANH THÍCH HỢP LOÈ THIÊN HẠ

1. You look at a star for two reasons, because it is luminous, and because it is impenetrable.
( Người ngắm vì sao là bởi hai lý do, bởi vì nó lấp lánh, cũng bởi vì nó không thể chạm tới)

2. You are the last rose in my barren land.
(Người là đóa hoa cuối cùng trên mảnh đất cằn cỗi của tôi)

3. I tried to disappear and no one asked.
(Tôi từng thử biến mất, nhưng lại không một ai quan tâm)

4. The world is dull,but it has you.
(Thế gian vô vị, nhưng nó lại có em.)

5. I’ve been looking for the spring of my life, you just smile.
(Tôi vốn tìm kiếm mùa xuân của đời mình, cho đến khi em tình cờ cười lên.)

6. The world is dark,and then you come,with the stars and the moon.
(Thế giới này vốn tăm tối, cho đến khi người xuất hiện, mang đến cùng trăng sao.)

7. One day, I'll find her. And when they ask me how I knew she was the one, I'll tell them, “Because she loved me in spite of all the unlovable pieces she had to pick up.”
(Rồi sẽ có ngày tôi tìm thấy cô ấy. Mọi người sẽ tò mò sao lại chắc chắn là người đó, tôi sẽ nói rằng "Bởi vì cô ấy yêu tôi, yêu trọn vẹn cả những điều không hoàn hảo của tôi.")

8. How to solve the worry , only rich.
(Làm sao để xóa sạch mọi ưu phiền, đó là trở nên giàu có.)

9. Better to light one candle than to curse the darkness.
(Nguyền rủa bóng đêm chi bằng tự mình thắp lên ngọn nến.)

10. I can bear any pain as long as it has meaning.
(Tôi có thể chịu đựng bất kỳ sự khổ sở nào, chỉ cần chúng có ý nghĩa.)

11. Be a pineapple. Stand tall，wear a crown，be sweet on the inside.
(Hãy sống như một trái dứa: dáng đứng hiên ngang, đầu đội vương miện, nhưng bên trong lại ngọt ngào.)

12. Nobody is stupid. It's just that sometimes, we choose to be stupid for us to feel a little bit of what they call happiness.
(Không ai là ngốc nghếch hoàn toàn. Có chăng là giả vờ khờ khạo, để cảm nhận một chút tư vị của hạnh phúc.)

13. You left in peace , and left me in pieces.
(Người nhẹ nhàng rời đi, bỏ mặc ta tan nát nơi này.)

14. Life is short. Smile while you still have teeth
(Cuộc đời này ngắn lắm. Hãy cười khi mà bạn vẫn còn răng)

15. The sun won't run to you, the moon won't, the stars won't, but I shall.
(Mặt trời sẽ không đến vì em, mặt trăng không, các ngôi sao kia cũng sẽ không, nhưng anh sẽ.)

16. In the story of your life, don’t let anybody else hold the pen.
(Câu chuyện cuộc đời của riêng bạn, đừng để ai nắm được chiếc bút.)

17▪ - "If I walk would you run？
If I stop would you come？
If I say you are the one，
Will you believe？"
(Nếu như anh cất bước, em có đi cùng không?
Nếu như anh dừng lại, liệu em có đến?
Nếu như anh nói em chính là duy nhất, em sẽ tin chứ?)

18. No matter where you are, or what you are doing, or who you with, I will honestly, truly, completely love you.
(Cho dù em đang ở đâu, đang làm gì, hay đi cùng ai, anh cũng sẽ thật lòng, thật lòng, hoàn toàn yêu em)

19. If you shed for stears when you miss the sun, you also miss the stars.
(Đừng khóc vì hoàng hôn, nếu không em sẽ bỏ lỡ cả những vì sao.)

20. There is a crack in everything，that's how the light gets in.
(Vạn vật đều có vết nứt, đó là nơi ánh sáng chiếu vào.)

21. Time would heal almost all wounds. If your wounds have not been healed up, please wait for a short while.
(Thời gian luôn chữa lành mọi vết thương. Nếu nó vẫn còn đau âm ỉ, thì hãy đợi thêm một lát nữa)

22. There's a difference between "love" and "like". If you like a flower you will pick it, but if you love a flower, you will water it every day.
(Luôn có sự khác biệt giữa "yêu" và "thích". Nếu thích một đóa hồng, bạn sẽ thẳng tay hái nó, nhưng nếu yêu, bạn sẽ tưới nước hằng ngày.)

23. Women's tears are useless, but you make a woman cry, it is useless!
(Nước mắt phụ nữ vốn vô dụng, nhưng làm họ khóc, thì bạn chính là đồ vô dụng!)

24. The secret of a good relationship is that you don't have to be serious, but you have to be serious!
(Bí mật để giữ gìn tốt một mối quan hệ chính là trong mối quan hệ đó bạn không cần thiết phải nghiêm túc, nhưng bạn nhất định phải nghiêm túc!)

25. I wish I were what I was when I wished I were what I am.
(Tôi ước gì có thể trở lại như ban đầu, mà ở thời điểm đó tôi đã ước được trở thành tôi của hiện tại.)

26. I am a Rich kid 🙂

Dịch bởi: Si Me Amas, Serva Me

📜 [專欄新文章] Uniswap v3 Features Explained in Depth

✍️ 田少谷 Shao

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

Once again the game-changing DEX 🦄 👑

Image source: https://uniswap.org/blog/uniswap-v3/

Outline

0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion

0. Intro

The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥

While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.

Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅

Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊

If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏

There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!

1. Uniswap & AMM recap

Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.

Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.

Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:

AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.

Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².

Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.

In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP

¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity

² the range is in fact [-∞,∞], while a price in most cases won’t be negative

³ AMM of constant sum does not have price slippage

2. Tick

The whole innovation of Uniswap v3 starts from ticks.

For those unfamiliar with what is a tick:

Source: https://www.investopedia.com/terms/t/tick.asp

By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:

The price range of each tick is predefined by the system instead of being proposed by users.

Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.

Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.

With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯

So, how is the price range of a tick decided?

This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.

The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.

Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.

However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.

This is how price ranges of ticks are decided⁴:

Image source: https://uniswap.org/whitepaper-v3.pdf

With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.

As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.

For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.

p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001

See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?

Image source: https://tenor.com/view/coin-master-cool-gif-19748052

But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?

Price range: max & min

To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.

Image source: https://uniswap.org/whitepaper-v3.pdf

The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.

24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:

1.0001 ^ (2¹⁸) = 242,214,459,604.341

1.0001 ^ -(2¹⁷) = 0.000002031888943

I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌

⁴ For implementation concern, however, a square root is added to both sides of the equation.

How about finding out which tick does a price belong to?

Tick index from price

The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:

Image source: https://www.codecogs.com/latex/eqneditor.php

Let’s try this out, say we wanna find out the tick index of 1000000.

Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm

Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!

⁵ This formula is also slightly modified to fit the real implementation usage.

3. Concentrated liquidity

Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.

Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.

As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!

Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/

Mmm… examples are always helpful for abstract descriptions 😂

Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].

If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.

The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.

However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).

We can observe the following two points from the above example:

Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.

√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.

What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!

Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!

Image source: https://uniswap.org/blog/uniswap-v3/

It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵

⁶ Thanks to Yenwen Feng for the information.

4. Range orders: reversible limit orders

As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:

current price < the targeted price range

current price > the targeted price range

current price belongs to the targeted price range

The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.

The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).

There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!

In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.

Range orders

To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.

The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.

For the price of X to go up, y has to increase and x decrease.

With this pricing mechanism in mind, it’s example time!

Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).

The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.

The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.

If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.

Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.

What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].

This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.

…wut? 🤔

Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!

What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.

The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.

Image source: https://uniswap.org/blog/uniswap-v3/

Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.

To wrap up such an interesting feature, we know that:

Only one token is required for range orders.

Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯

I will be discussing more the impacts of v3 in 5. Impacts of v3.

⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.

Reversible limit orders

As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.

We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].

Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.

The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.

As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:

When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸

When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸

A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!

⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.

5. Impacts of v3

Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:

Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.

The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.

LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏

In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.

After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔

Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!

6. Conclusion

That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂

There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅

If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!

Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟

Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

👏 歡迎轉載分享鼓掌

The political environment is complicated by the potential for military conflict should Taiwan make overt actions toward de jure independence; it is the official PRC policy to use force to ensure reunification if peaceful reunification is no longer possible, as stated in its anti-secession law, and for this reason there are substantial military installations on the Fujian coast. However, in recent years, the PRC has moved towards promoting peaceful relations, including stronger economic ties, with the current ROC government aimed at unification through the one country, two systems formula or maintaining the status quo under the 1992 Consensus.

On 29 April 2005, Kuomintang Chairman Lien Chan travelled to Beijing and met with Communist Party of China (CPC) Secretary-General Hu Jintao, the first meeting between the leaders of the two parties since the end of the Chinese Civil War in 1949. On 11 February 2014, Mainland Affairs Council Head Wang Yu-chi travelled to Nanjing and met with Taiwan Affairs Office Head Zhang Zhijun, the first meeting between high-ranking officials from either side. Zhang paid a reciprocal visit to Taiwan and met Wang on 25 June 2014, making Zhang the first minister-level PRC official to ever visit Taiwan. On 7 November 2015, Ma Ying-jeou (in his capacity as Leader of Taiwan) and Xi Jinping (in his capacity as Leader of Mainland China) travelled to Singapore and met up, marking the highest-level exchange between the two sides since 1949.

The PRC supports a version of the One-China policy, which states that Taiwan and mainland China are both part of China, and that the PRC is the only legitimate government of China. It uses this policy to prevent the international recognition of the ROC as an independent sovereign state, meaning that Taiwan participates in international forums under the name "Chinese Taipei". With the emergence of the Taiwanese independence movement, the name "Taiwan" has been employed increasingly often on the island.

What is the difference between Mainland China and Taiwan? Come find out and make a choice as to where you'd like to travel or live...

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