Comment on So much

davidagain@lemmy.world ⁨3⁩ ⁨months⁩ ago

I don’t think you can use the x0 plus minus delta in the bracket (or anywhere), because then the function that’s 1 on the rationals and 0 on the irrationals is continuous, because no matter what positive number epsilon is, you can pick delta=7 and x0 plus minus delta is exactly as rational as x0 is so the distance to L is zero, so under epsilon.

You have to say that whenever |x - 0x|<delta, |f(x) - L|<epsilon.

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