Infinity, represented as ∞ is a concept in mathematics and philosophy that refers to a quantity without any bound. Infinity is a strange concept, and has many intriguing implications.

• A subset of an infinite set can be put into one-to-one correspondence with the original set. For example, the set of natural numbers and the set of even numbers are in one-to-one correspondence, even though the set of even numbers is a subset of the set of natural numbers. This rejects the concept that the whole cannot be the same size as the part.
• The paradoxical nature of infinity can be illustrated using the idea of a grand hotel, which has infinitely many rooms, and all of them are filled with guests. Yet, a new guest can be accommodated by moving each of the existing guests, one by one, to the other rooms.
• There exist different types of infinities. The infinity of natural numbers is different from the infinity of real numbers, for example. The set of naturals is countably infinite, while the set of reals is uncountably infinite.
• The real line is the same size as any of its non-zero segments.  For example, the set can be put into one-to-one correspondence with the set by defining a function that maps to . One example of such a function could be
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• If there are different kinds of infinities, one might think that there will exist a biggest infinity. However, that’s not true. It can be mathematically proven that whatever infinity one might create, there will exist a bigger infinity.
• Infinities have very interesting roles in cosmology. One question that physicists face is whether physical infinities actually exist. Is the universe finite, something like the earth, so that if you start moving from one point you will eventually return to that point again, or is it unbounded, so that you can keep moving in some direction for infinite time? Does space go on forever is an important question in cosmology.
• Another question facing physicists is whether time is infinite or not. Has time always existed – or was there some initial point of time, . Our present universe might keep on expanding forever, like it is doing presently, in which case we have an infinite amount of time ahead of us, or it may reverse its expansion, start contracting and end in a big crunch, which would effectively end time.

Perhaps the finite human mind will never be able to grasp the concept of infinity completely. George Cantor, one of the world’s leading mathematicians who worked on infinity, once said: “I see it, but I don’t believe it”.