Uniform continuity

Uniform continuity cannot depend on x, the order is different. Continuity depends on points, but in uniform_continuity the point has less power to due things, therefore x is chosen after a width is made (delta) and a height. %%visits: 2

∀ϵ > 0∃δe > 0

Non examples of uniform_continuity (but continuity)

$f(x) = \frac{1}{x}$ on (0,1)

In uniform_continuity, the graph cannot keep getting steeper.

uniform_continuity that escapes to vertical infinity, or escape at a boundary.

uniform_continuity:~ When the delta is not dependant on x

uniform_continuity

introduction

intuition

rigour

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examples and non-examples

example sinx

non-example $\frac{1}{x}$

The asymptote at x = 0 is what makes the function $y=\frac{1}{x}$ not be uniformly continuous ## resources tags :math:real_analysis:

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