Proof: x^2 is NOT uniformly continuous

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In this video we prove that the function "x squared" is NOT uniformly continuous. We first briefly discuss the definition of uniformly continuous, then talk about how we can negate that in order to prove that the function in question is NOT uniformly continuous. Then we talk about how it is sometimes fruitful just to dive in to a sort of "standard form" of such a proof and to make the exact definitions that you need after it has become apparent what they need to be.
Correction 1:31: This should not be an implication arrow but rather an "and". That is, we need to show that |x-y| is less than delta AND |x^2-y^2| is greater than or equal to epsilon.
  1. mathAHA
  2. uniform continuity
  3. mathematical analysis
  4. x squared is not uniformly continuous
  5. standard proofs
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Correction 1:31: This should not be an implication arrow but rather an "and". That is, we need to show that |x-y| is less than delta AND |x^2-y^2| is greater than or equal to epsilon.

mathaha
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Hi thank you for the video! Im not sure why ``y'' can can depend on \epsilon (last part setting delta y = \epsilon). since we fixed epsilon at the very beginning? also, it seems that we are proving a stronger negated statement: instead of exists epsilon blabla, we are proving for all epsilon blabla if we allow y to depend on epsilon. Any help is greatly appreciated!

seantu
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All i know is that when you rotate the x, y plane with x² on it in such a way given an x, y, z plane, x² becomes a circle 💀

crimsonbreadcat
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so are we basically proving that x^2 does not grow linearly?

gm