What is the largest number? Any number that is offered can be bettered by that number plus 1. A common answer is infinity, although infinity isn't a specific number. "Infinite" describes something that is without bounds. Something could be infinitely large (set of integers) or something could be into infinitesimally small (as done in calculus).
Another approach to this question of the largest number is to ask what is the largest number used in a proof. In 1977 the mathematician Ronald Graham established the world record for the largest specific integer used in a mathematical proof. Graham's number is so large that if all the atoms in the universe were made into ink, the number could not be written. That is certainly disappointed for the readers of this post who wanted to see the number.
However, the last digits of Graham's number are: ...262464195387.
The actual expression of Graham's number uses hyperoperators which are higher order forms of exponentiation.
Since 1977, Graham's number has been exceeded by larger super-numbers used in proofs. One example is TREE(3).
Ronald Graham passed away in 2020 and was honored in a Numberphile podcast. An earlier podcast specifically described Graham's number. While the end digits of Graham's number have been determined, the first digit is unknown. Graham was asked what digit he would like it to be and he said he actually knew the first digit but only when the number is expressed in base-2 and then it is 1.
The icon I chose for this post is juggling because Ron Graham was an accomplished juggler. For a photo of Graham, see New York Times Obituary Link with photo.
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