I'm thinking that a stock marketer uses integers to symbolize if a stock has gone up or down.
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Every aspect of mathematics depends upon integers, and even if you don't do any mathematics, you count things with integers. If you even want to know how many guests you are having for dinner, you need to use integers.
You can sometime use integers but often speed or velocity can also be irrational.
Yes.
Yep.
You can use them for counting, which is in fact addition. You can also use them for subtracion. Integers are natural numbers. This means you don't use decimals or fractions.