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What Is The Largest Number?

Graham's Number

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What Is The Largest Number?

Humans have been using numbers for thousands of years. It is believed that the concept of numbers first originated when prehistoric humans began using their fingers to count. This eventually evolved into sign language and then tally marks on objects like sand, walls and sticks.

We’ve come a long way. Now we use calculators and computers to count our large numbers. We even have a word for numbers that are without a limit. Sometimes, it seems like the only people who can make sense of it all are the mathematical savants. One reader wanted to know: What is the largest number in mathematics?

Not So Obvious

So what’s the largest number? The answer should be pretty obvious. Infinity, right? But that’s not entirely correct.

Infinity in the strictest sense, is not a number at all. It’s a concept. An idea. And a mind bending one at that. Infinity is a concept which means “a quantity without bound or end”.

The definition of infinity in mathematics states that no matter how big a number is, you can always add 1 to it, and it becomes larger. By continually doing this, a number can always get larger – forever, or “infinitely”.

What is the largest number ever used?

The concept of infinity

The largest number ever used in a mathematical proof is Graham’s number. It is currently listed in the Guinness Book of Records as the world’s largest number.

Graham’s number is the upper bound solution to a very exotic problem in Ramsey theory. A theory which attempts to solve the question, “What is the smallest dimension n of a hypercube such that if the lines joining all pairs of corners are two-colored, a planar complete graph K4 of one color will be forced?” It’s not a question that rolls off the tongue easily.

Graham’s number is so large, that even mathematicians have difficulty even comprehending it. It makes other, more well-known large numbers like googol or a googolplex child’s play by comparison. It’s may be difficult to conceptualize, but Graham’s number is so large, that if you took all the known material and matter in the universe, converted it to ink and put it in a pen, there would not be enough ink to write the number down on paper.

So what was the answer to Graham’s problem? According to opinions of the experts in Ramsey theory, they suspect that the answer is “6”.

Graham, R. L.; Rothschild, B. L. (1971). “Ramsey’s Theorem for n-Parameter Sets”
David Wells. The Penguin Dictionary of Curious and Interesting Numbers. Penguin. 1986
Gardner, M. “Mathematical Games.” Scientific American, 237, 18-28, Nov. 1977.



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