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A collection of 7 posts

The Infinite Monkey Theorem

big numbers Featured

The Infinite Monkey Theorem

The infinite monkey theorem is a bar [http://www.theinfinitemonkeytheorem.com/] in Austin, TX, but it is also a very cool mathematical theorem that deals with very big numbers. This article is about the theorem which has become very popular in recent times. The theorem as I understand it is

1+2+3+4+... = -1/12

1+2+3+4+... = -1/12

This is a remarkable and hard to believe consequence in mathematics. If you were to sum the natural numbers all the way to infinity, you would get \(-\frac{1}{12}\). $$ 1+2+3+4+5+6... = -\frac{1}{12} $$ This is just insane. It makes no sense that

Graham's number - big numbers blow my mind!

Graham's number - big numbers blow my mind!

One of the most famous big numbers in mathematics is Graham's number. For a while it was the largest number ever used in a legit mathematical proof. That isn't the case anymore but it is still a legend. The number is the upper bound to a

The longest finite time ever calculated by a physicist

The longest finite time ever calculated by a physicist

I've written quite a bit on big numbers [https://josh.kerr.dev/tag/big-numbers/] because I find them fascinating. Two of the areas where you find interesting big numbers are astronomy and cosmology. For example the observable universe is thought to be 93 billion light years across (That&

The Ackermann function explained

The Ackermann function is a recursive function originally invented by Wilhelm Ackermann [https://en.wikipedia.org/wiki/Wilhelm_Ackermann]. It is one of a series of mathematical functions that quickly generates enormous numbers. If you haven't read my article on Knuth's up arrow notation [http://www.

Knuth's up arrow notation explained

When we talk about large numbers, we are talking about numbers that are bigger than what we use in our ordinary day to day life. These are numbers typically used by mathematicians in fields such as cosmology, cryptography and statistical mechanics. Since big numbers have a lot of digits, it

How big is googol?

Googol is a big number. The search engine was famously named after it. There are several ways that we can think about Googol. Written with exponents, the number can be represented like so: $$ 10^{100} $$ If you expand it out you would write a 1 followed by 100 zeros: 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000