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How Many Numbers Are There?

Sarah Jenkins • • 5 min read
How Many Numbers Are There?

How many real numbers are there? One answer is, "Infinitely many." A more sophisticated answer is "Uncountably many," since Georg Cantor

Georg Cantor
He created set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers.
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proved that the real line -- the continuum -- cannot be put into one-one correspondence with the natural numbers.

Do numbers ever end?

The sequence of natural numbers never ends, and is infinite. ... So, when we see a number like "0.999..." (i.e. a decimal number with an infinite series of 9s), there is no end to the number of 9s. You cannot say "but what happens if it ends in an 8?", because it simply does not end.

What is the largest number?

The biggest number referred to regularly is a googolplex (10googol), which works out as 1010^100. To show how ridiculous that number is, mathematician Wolfgang H Nitsche started releasing editions of a book trying to write it down.

Sarah Jenkins
Author

Sarah Jenkins

Sarah Jenkins is a veteran tech journalist with over 12 years of experience covering artificial intelligence, mobile innovations, and digital ethics. Her insights have appeared in leading technology publications worldwide.