latex greater than的八卦，YOUTUBE和Yahoo名人娛樂都在討論

這是我見過最好最實用的防疫文章！
請耐心看完並力行實踐！
保護自己，家人及他人！
James Robb, MD UC San Diego. 詹姆斯.蘿蔔，加州大學聖地亞哥分校醫學博士

Subject: What I am doing for the upcoming COVID-19 (coronavirus) pandemic
新冠疫情擴散下我的防備攻略

Dear Colleagues, as some of you may recall, when I was a professor of pathology at the University of California San Diego, I was one of the first molecular virologists in the world to work on coronaviruses (the 1970s). I was the first to demonstrate the number of genes the virus contained. Since then, I have kept up with the coronavirus field and its multiple clinical transfers into the human population (e.g., SARS, MERS), from different animal sources.
眾所周知，我是冠狀病毒的分子病毒專家，從70年代到現在一直在研究這些病毒。所以我是有發言權的。

The current projections for its expansion in the US are only probable, due to continued insufficient worldwide data, but it is most likely to be widespread in the US by mid to late March and April.
現在大規模在美國爆發還只是一個可能，現在還是數據不足。但是廣泛傳播要到三月底四月份。

Here is what I have done and the precautions that I take and will take. These are the same precautions I currently use during our influenza seasons, except for the mask and gloves.
我預防冠狀病毒的方法和防止流感一樣，只是增加口罩和手套。

1) NO HANDSHAKING! Use a fist bump, slight bow, elbow bump, etc.
不要和別人握手。用碰拳頭，小鞠躬，碰胳膊肘等代替。

2) Use ONLY your knuckle to touch light switches. elevator buttons, etc.. Lift the gasoline dispenser with a paper towel or use a disposable glove.
只用手指關節去開燈的開關和電梯按鈕。用紙或者戴手套加汽油。

3) Open doors with your closed fist or hip - do not grasp the handle with your hand, unless there is no other way to open the door. Especially important on bathroom and post office/commercial doors.
不要用手抓門把，特別是公共廁所，郵局，商業中心的門。用拳頭和屁股把門撞開。

4) Use disinfectant wipes at the stores when they are available, including wiping the handle and child seat in grocery carts.
如果店裡有抗菌濕巾提供，用它來擦所有碰到的把柄和兒童座。

5) Wash your hands with soap for 10-20 seconds and/or use a greater than 60% alcohol-based hand sanitizer whenever you return home from ANY activity that involves locations where other people have been.
每次從外面回家，至少用肥皂洗手20秒。

6) Keep a bottle of sanitizer available at each of your home's entrances. AND in your car for use after getting gas or touching other contaminated objects when you can't immediately wash your hands.
在家裡的門口和車里放一瓶消毒液。

7) If possible, cough or sneeze into a disposable tissue and discard. Use your elbow only if you have to. The clothing on your elbow will contain infectious virus that can be passed on for up to a week or more!
如果來得及，盡量打噴嚏擤鼻涕到紙巾上。如果來不及用胳膊肘捂了，要及時換衣服。

What I have stocked in preparation for the pandemic spread to the US:
在美國家裡，我囤積了一下物資：

1) Latex or nitrile latex disposable gloves for use when going shopping, using the gasoline pump, and all other outside activity when you come in contact with contaminated areas.
一次性橡皮手套，外出時備用。

Note: This virus is spread in large droplets by coughing and sneezing. This means that the air will not infect you! BUT all the surfaces where these droplets land are infectious for about a week on average - everything that is associated with infected people will be contaminated and potentially infectious.
注意，病毒靠咳嗽和打噴嚏產生的較大的水霧珠傳播的，不是因為空氣本身。所有的水霧珠會落在各種各樣的表面，在那裡呆一個星期之久。所有感染的人碰過的東西都有病毒。

The virus is on surfaces and you will not be infected unless your unprotected face is directly coughed or sneezed upon. This virus only has cell receptors for lung cells (it only infects your lungs) The only way for the virus to infect you is through your nose or mouth via your hands or an infected cough or sneeze onto or into your nose or mouth.
這個病毒只會感染你的肺，而進入的途徑就是你的口鼻。所以唯一被感染的機會是你的手帶到你的口鼻除非有人直接對著你的臉打噴嚏咳嗽。

2) Stock up now with disposable surgical masks and use them to prevent you from touching your nose and/or mouth (We touch our nose/mouth 90X/day without knowing it!). This is the only way this virus can infect you - it is lung-specific. The mask will not prevent the virus in a direct sneeze from getting into your nose or mouth - it is only to keep you from touching your nose or mouth.
在家裡儲存一些一次性醫用口罩。其實口罩並不是用來防止別人對你打噴嚏，而是阻止你的手老是去碰你的口鼻。你可能不知道，我們每天不知不覺會碰自己的口鼻90次以上。

3) Stock up now with hand sanitizers and latex/nitrile gloves (get the appropriate sizes for your family). The hand sanitizers must be alcohol-based and greater than 60% alcohol to be effective.
儲存一些洗手消毒液，最好是含有有60%以上酒精那種及買一些手套。

4) Stock up now with zinc lozenges. These lozenges have been proven to be effective in blocking coronavirus (and most other viruses) from multiplying in your throat and nasopharynx. Use as directed several times each day when you begin to feel ANY "cold-like" symptoms beginning. It is best to lie down and let the lozenge dissolve in the back of your throat and nasopharynx. Cold-Eeze lozenges is one brand available, but there are other brands available.
儲備大量的鋅錠劑。一般的藥店應該有很多選擇。其中一種叫Cold-Eeze lozenges。鋅錠劑被證實對冠狀病毒和其他病毒有一定防治作用。當你開始感到有感冒的感覺到時候，按照說明書每天服用數次。最好安靜的躺下來，讓鋅錠劑慢慢融化在喉嚨和鼻腔里。

I, as many others do, hope that this pandemic will be reasonably contained, BUT I personally do not think it will be. Humans have never seen this snake-associated virus before and have no internal defense against it. Tremendous worldwide efforts are being made to understand the molecular and clinical virology of this virus. Unbelievable molecular knowledge about the genomics, structure, and virulence of this virus has already been achieved. BUT, there will be NO drugs or vaccines available this year to protect us or limit the infection within us. Only symptomatic support is available.
和大家一樣，我希望冠狀病毒的疫情能夠得到控制。科學界已經學到很多關於這個病毒的東西。可是畢竟人類沒有見過這個病毒，也沒有建立對它的免疫力。我不認為一年內會有真正有效藥物和疫苗開發出來拯救人類或者控制病毒。目前只能減緩病狀。

I hope these personal thoughts will be helpful during this potentially catastrophic pandemic. You are welcome to share this email.
Good luck to all of us.
Jim

我希望我這樣個人的想法對你有所幫助。歡迎你和大家分享這份文章的內容。
祝我們好運！詹姆斯
James Robb, MD FCAP

📜 [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

pic taken at cosmetic-candy=)...seriously an addict for brushes!!!haha


The make-up brush sets you have should contain the right set of tools. This is essential to good make-up application and great looks because it really makes applying make-up so much easier.

A professional collection of different-sized brushes allows you to apply eye and lip colors more easily and blend them in smoother.

And, did you know that using the right sponge helps to smooth on foundation more easily and evenly?!

So making a small investment in a few good, affordable, natural-bristle make-up brush sets is indispensable.

Taking Care Of Your Make-Up Brush Sets...


To keep the brush applicators in your make-up brush sets helping you look good for a very long time it's a good idea to take good care of them. They would love to be stored neatly in a makeup box, maybe even a special tool box of their own. Don't leave your cosmetic brush unattended in your powder room. You never know what they might get into! Good faithful brushes, stored properly, can spend their useful lifetime with you!

While looking for a few good brushes for your make-up brush sets, you should try them before taking them home. A brush with soft bristles works best for soft looks, but it can't be too soft or it won't pick up the color. Now, if it's too hard, it will feel scratchy and it may even irritate your skin. Avoid cheap discount brushes.

Also, you don't want the brushes in your make-up brush sets going bald on you after you adopt them, so try this; if the unfortunate brush looses more that a few hairs when you run it along the back of you hand, don't take it home. And if more than a few come off when you gently pull on the bristles, leave the brush behind.

Which Brushes To Have In Your Make-Up Brush Sets?...

Retractable Powder Brush
This is one of the largest brushes in your make-up brush sets and it's used to apply loose face or bronzing powder (mineral powder) evenly. Use the same brush to dust off the excess powder from your face (same size as kabuki brush except with a handle).

Round Powder Brush
Same as above except for the rounded handle and fan style bristles which allows for a wider single application.

Eyebrow Brush / Eyelash Comb (Lash Separator)
This two-tools-in-one is the one to use for brushing eyebrows up and outwards to give definition to your eyebrow. Use the eyelash comb to separate eyelashes and for combing out excess mascara from your eyelashes after it dries to prevent clogging.

Angled Eyebrow Brush
Sometimes this brush is used in combination with an eyebrow pencil to darken your eyebrows or to fill in spaces where the hair growth may be uneven. Choose sable hair for fine eyebrows are and hog hair for coarse eyebrow hair.

Mascara Wand
Use the mascara wand (included with mascara set) to apply your mascara. When needed, comb through your lashes using the eyelash comb to remove excess mascara and give your lashes and even look. A must for make-up brush sets.

Dome-Shaped Eye Shadow Brush
This type of brush's hair is graduated from short to long in a rounded, dome shape (eye crease brush). You should use a different brush per different application (example; one to shade, another to highlight). The neat thing about this brush is that, because of it's rounded cut, the shadow clings to the brush in such a way that is allows the particles of shadow to be distributed evenly across the eyelid. They are available in different sizes. Another must for your make-up brush sets.

Flat Eye Shadow Brush
This brush (eye definer) is used to blend in the color only and should not be dipped into the powder, shadow or blusher at all. This type isn't as good for applying powder or eye shadow since it doesn't allow the color to be distributed gradually.

Smudge Brush
This is the perfect brush for applying eyeshadow close to the lash line for a smoky lined eye. An ideal brush to smudge or soften pencil lines or to place powder over pencil for added depth and wearability.

Blusher Blending Brush
Can be larger than your blusher brush (cheek brush) and the hair can be either rounded or straight cut. Use this brush to soften the edges after applying blusher. And never dip it into your blusher container, this brush is strictly for blending the blusher on your face.

Retractable Lip Brush
Must definitely be a small firm-tipped brush (lip color brush) to ensure a perfect lip line and give you greater control over applying lip color. Of course, you could still achieve a clean lip line by carefully using an average-sized brush. A must for make-up brush sets.

Foundation Sponges
Sponges allow you to get into creases easier and they help avoid streaks when applying liquid foundation because sponges apply cake powder lightly and evenly. They need to be replaced when they look shiny because they pick up oils on your face. Latex sponges are available in a variety of shapes and forms. Keep sponges clean by washing them once a week. Sponges are an important addition to make-up brush sets (good for applying concealer).

Makeup Brush Set
This kit ontains a collection of seven best-selling professional wood-handle makeup brushes including:

Eyebrow brush
Eyeliner brush
Eye shadow brush
Eye crease brush
Blusher blending brush
Blush brush
Lip brush

Some good brands include: Mac, Bobbi Brown and Sigma.