Why did mathematicians conceptualized infinity? Do they use it in any mathematical systems?
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The other folks already explained how it exists in something like calculus but I’ll explain why it exists.
Infinity as a concept is something that has to exist. You could compare it to “forever”, used in time, if something never ends it is forever, if a number goes on forever it is infinite.
Imagine if the number one was added to itself or anything else, any additive operation too. We would have to say that number is infinite, because there is no end to the operation. this is also true inversely if we subtract because there is both a positive and negative infinity.
We can also look at decimal places. The number 2 can be represented as the integer 2, or 2.0, or 2.000000000000, you can add as many zeroes as you want, this also applies to numbers in-between 2.5, is the same as 2.50000000. that is why there is a infinite amount of numbers between 2 and 3, and there’s also a larger infinite amount between 1 and and 100.
Infinite existing is really the only way to explain something like this. Imagine if the concept of “forever” didn’t exist, if an event is ongoing, and never stops it’s not entirely true to say it’ll just go on for a really long time, because it will go on forever.
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