Science Forums 2

[CraigD]

Originally Posted by Jet2

Can any maths experts explain to me about this?
Are infinite large and infinite small the same?

I’d say “no”, but note that one can be written as an arithmetic expression using terms of the other.

Since the most popular numbers have a sign – positive or negative – you can speak of or . Since most of the most interesting math about involving infinity tends to consider it a cardinal number – the count of elements of a set – most mathematicians consider and to be just slightly different “flavors” of the same concept.

“Infinitely small” might be taken as a synonym for “infinitesimal”, and written something like . In ordinary language, an infinitesimal is a number closer to zero than any other, yet not equal to zero. They’re a very important concept in calculus – you might reasonably call them “the essence of calculus”, where they’re written (sort of) with “d”, as in or . Infinitesimals, and whether it’s a good idea to use the word or think of them as somehow conceptually real, have provoked centuries of discussion among mathematicians.

Infinity is one of the central, deep concepts of math and philosophy, so doesn’t lend itself to the sort of short answers I’ve given above. In my experience, you have to read and think about it a good bit to begin appreciating its history and significance – and will find doing so a pleasant and rewarding experience - though YMMV.