Eli5 Can someone tell me why some studies and mathematicians bother with the concept of infinite?
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“Bother”? It’s unavoidable.
The integers already form an infinite set.
The concept of limit, central to analysis, relies on it: what happens if we go past any bound, or make an infinite number of ever smaller steps? And that’s where the interesting things happen.
Finite objects can’t capture all of mathematics. For example finite-dimensional vector spaces (e. g. little arrows in the plane and such) are very nice but if you want to study functions from that point of view you have to do it in infinite-dimensional spaces. And again, you get new, interesting properties.
Even very classical geometry like the study of conics (circles, ellipses, parabolas and hyperbolas), which goes back to the Greeks, needs a line at infinity to become complete, removing exceptions you can’t get rid of without such an “ideal concept”.
Rest assured that with a bit of practice the infinite becomes quite familiar.
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