Def for R

For sequence (𝑥𝑛), we can say it’s bounded if

(𝑀>0)(𝑛)|𝑥𝑛|<𝑀

Def 23.5

A set 𝑆𝑋 is called bounded if there

(𝑅>0)(𝑥𝑋)𝑆𝐵𝑅(𝑥)

Where 𝐵𝑅 is a Delta-ball.

Def

If we say a function is bounded, we can say

(𝑀>0)(𝑥)|𝑓(𝑥)|<𝑀