A function f : A ->R is increasing if f(x) <= f(y) for every x, y in A such that x <= y.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that f : [a, b] -> R is increasing and that a < c < b.

i want to shat that :

lim f(x) = sup{f(x) | a <= x < c} and

x->c-

limf(x) = inf{f(x) | c < x <= b}.

x->c+

and whether these limits are the same?

can anyone help with this

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Increasing funtion

**Physics Forums | Science Articles, Homework Help, Discussion**