Where do mathematical inequalities come from?

[Terrell]

what do you think are the inspirations or motivations that lead to inequality statements like am-gm, bernoullie's inequality, etc...? are they inspired by physics, engineering...? learning them for the first time made me wonder where they came from. thanks!

 

[Simon Bridge]

Inequality statements are inspired by the desire to communicate.
Every time you want to say that something occupies all values up to (and maybe including) a certain one, you will need an inequality statement.
Like, I am working all "days from now up to next thursday inclusive" is an inequality statement.

 

[symbolipoint]

Simon Bridge's response makes so good sense that I want to apply TWO "like"s to it but doing so only cancels the first "like".

 

[Simon Bridge]

Maths is a language ... :)

 

[Simon Bridge]

For instance:
If d is a day in which I am working, and today is day a, and "next Thursday" is day t, then I am working: $a\leq d \leq t$
If I start work tomorrow, instead, then $a < d \leq t$ ... it's a nice short way to write it down.
If my days are numbered (and I don't count parts of days) then $a < d \leq t$ is the same as $a+1 \leq d \leq t$ because a+1 will be the day after today.