[gertef]

The measure of epsilon is 0.

Proof: what else could it be? If it's not 0, there's a smaller number, contradicting your (intuitive) definition of epsilon.

[CuriouslyC]

Wouldn't it be more accurate to describe epsilon as an infinitesimal?

[alexbecker]

There are no infinitesimals in the reals. You can define a mathematical structure containing infinitesimals [0], but it's not the reals.

[0] Specifically, the dual numbers: https://en.wikipedia.org/wiki/Dual_number

[CuriouslyC]

Interesting. How do you describe the difference between two successive real numbers?

[stymaar]

> How do you describe the difference between two successive real numbers?

There is no such things as «two successive real numbers».

[alexbecker]

Yeah, there aren't even two successive dual numbers. What's after 1? If it's 1 + epsilon, then what about 1 + epsilon / 2?