Two sets of numbers that have each number has a number that matches with it in the other set.
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A bijection is a one-to-one correspondence in set theory - a function which is both a surjection and an injection.
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Yes, they can be put into a one-to-one correspondence. The size of both sets is what's called a "countable infinity".
An infinite set whose elements can be put into a one-to-one correspondence with the set of integers is said to be countably infinite; otherwise, it is called uncountably infinite.
There are several infinities--one is "aleph null" which is a one to one correspondence with the set of natural numbers. It is written in Hebrew and I don't have the font. There is "aleph one" which may correspond to the continuum of real numbers--a "higher level of infinity". There may be more....