Biggest number in computer ever

Question

Just asked by my 5 year old kid: what is the biggest number in the computer?

We are not talking about max number for a specific data types, but the biggest number that a

Answer 1

I think you should be very proud that your 5 year old is already asking questions like this. And you should continue to promote that! This is truly amazing! With that said, I would say that saying Infinity does not count is thinking incorrectly about what numbers mean in computer memory. I feel like this way of thinking is a handicap.

Mathematicians will never be able to write out ALL the digits of pi or eulers number, BUT we FULLY understand it. Pi, as an example, is perfectly represented by infinite this series: (Pi / 4) = 1 - 1/3 + 1/5 - 1/7 + 1/9 - …
Just because you literally can’t go to inf. or print every single digit in a console means nothing. You could have printed the symbol representing pi and therefore capturing the inf. series. Computer Algebra Systems (CAS) represent numbers symbolically all the time. Pi, for instance, may be a Symbolic object in memory (the binary in memory did not DIRECTLY represent the number. It represents an "mathematical algorithm" for producing the answer to arbitrary precision). Then you do some math with it, transforming from one expression to the next. At no point in time did we not represent the number COMPLETELY.

At the end, you can do 2 things with this:

A) Evaluate the expression, turning it into a number of some kind (or Matrix or whatever). BUT this number could very well be an approximation (say like 20 digits of pi).

B) Keep it in its symbolic form for reference. Obviously we don’t like staring at symbols because we need to eventually turn the nobs on the apparatii. NOTE: sometimes you can get a finite (non-irrational) number perfectly represented in memory (like number 1) by taking limits or going to inf. Not literally having an inf. number in memory, but symbolically representing it. Just throw this in Wolfram alpha: Lim[Exp[-x], x --> Inf]; It gives you the number 0. Which is EXACT.

In short:

It was the HUMANS need to have some binary in memory that DIRECTLY represented the number that caused the number to degrade. Symbolically it was perfectly represented. You could design some algorithm that just continues to calculate the next digits of pi or eulers number giving you an arbitrary amount of precision (Now, this is obviously not practical of course).

I hope this was at least somewhat useful or interesting to you, even if you disagree =)