Examples of using Epsilon in English and their translations into Thai
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So then this simplifies to-- this right there simplifies to-- the absolute value of 3x minus 3 is less than epsilon.
And the reason why this is a proof, is because it shows no matter what epsilon you give me, I can always find a delta.
If you divide both sides of the equation by 3, you get the absolute value of x minus 1 is less than epsilon over 3.
So it's like, this is true, as long as the distance between x and 1 is less than epsilon over 3.
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We have just proved that the absolute value of essentially 3x times x minus 1 over x minus 1 minus 3 is less than epsilon, if and only if x minus 1 is less than epsilon over 3.
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At a party at Alpha Epsilon Pi.
But you might know us as the Epsilon Society.
So I have to prove, you give me an epsilon, that.
I submitted to the Epsilon Society when I was a kid. The Tech-Men's SmartMark is based on research.
This little symbol right here denotes membership, it looks a lot like the Greek letter epsilon, but it is not it just means membership of a set.
And it's like, oh, well as long as delta is that, you give me an epsilon, I can just apply that, you know, take epsilon and divide it by 4, or whatever.
So all we're saying, we just proved that-- so if you said that you wanted to be within 1 of our limit point, that's like you giving me an epsilon of 1.
If someone writes this they mean that you can give them any epsilon greater than 0, and then they will give you a delta-- remember your epsilon is how close you want f of x to be to your limit point.
It says this means-- and this is the epsilon delta definition of limits, and we will touch on epsilon and delta in a second, is I can guarantee you that f of x, you give me any distance from I you want.
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And for any epsilon you give me, any real number-- so this is, this would be I plus epsilon right here, this would be I minus epsilon right here--the epsilon delta definition of this says that no matter what epsilon one you give me, I can always specify a distance around a.
And epsilon can just be any number greater, any real number, greater than 0.
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