# Thread: The biggest number is Mathematics

1. A googol is 10^100 (10 with 100 zeroes after it)

A googolplex is 10^100^100 (10 with a googol of zeroes after it) - so big infact that there is not enough space in the known universe to write it down.

However; I have come up with the ULTIMATE BIG number. I call it the "Hopkiplex" (named after me; (who thought it up) - naturally)

The Hopkiplex is a googolplex to the power of a googolplex; a googolplex of times...i.e. googolplex^googolplex^googolplex^googolplex.....et c....

The short way of writing down the Hopkiplex will be "hPx" (A lowecase "h", and an upper "P" and a lowercase "x")

2.

3. I then invent the KALSTERPLEX, which is a Hopkiplex to the power of a Hopkiplex. 8)

4. Originally Posted by KALSTER
I then invent the KALSTERPLEX, which is a Hopkiplex to the power of a Hopkiplex. 8)
You just HAD to didn't you? :P

5. and i invent the smallest number which is one divided by a kalster

6. Perhaps the arrow notation would be a simple way of expressing your number.

http://en.wikipedia.org/wiki/Knuth's_up-arrow_notation

Where the second Googolplex is the number of powers in the power-tower of the first Googolplex raised to itself. I think the number of powers includes the base as well, so really there are (Googolplex - 1) actual powers in that expression. So I think your number might then be:

One a side note, how about the....

7. The more interesting thing is that no matter how big of a number we invent, there is always numbers too big to be invented.

Let's see. Define and , then:
F(0) = 2
F(1) = 4
F(2) = ???
F(3) = too big

Seriously, even calculating F(2) is difficult. I think F(3) or F(4) is bigger than the SuperBigPlex though.

8.

9. That's a pretty big number.

10. Okay,

so we now have:

googol
googolplex
hopkiplex
kalster
superbigplex

any more?

11. Superduperkalsterplex. It is a Kalsterplex to the power of the previously declared highest number, including iterations of itself. 8)

12. I give up.

Having said that though, I think I have worked out that it is impossible to multiply or square infinity.....

Lets assume we live in a multiverse and there are an infinite amount of possibilities that could make up a universe. Does this mean that the chance of a repeating universe is zero? - I think so, as possibilities are infinite, I cant see one being able to repeat...

Now think of finite possibilities; eventually they would have to repeat, and do so an infinite amount of times....

So then, I think that this means that infinity^2 is impossible, and thus infinity itself must be one-dimensional or even zero-dimensional. Therefore a singularity could be said to be infinite.

** Please note - I am aware that I may get ripped to shreds to mentioning any of the above; but go on go for it ! - Just as long as responses are academic **

13. Your description doesn't really work because infinity isn't a number. You can't do normal operations on it. There are times and places where it makes sense to do things like , but that's outside the realm of real arithmetic. In general, it's safest to consider infinity as a concept related to, but distinct from, numbers.

14. Originally Posted by MagiMaster
Your description doesn't really work because infinity isn't a number. You can't do normal operations on it. There are times and places where it makes sense to do things like , but that's outside the realm of real arithmetic. In general, it's safest to consider infinity as a concept related to, but distinct from, numbers.
Not really.

There is quite a theory of cardinal and ordinal numbers, including an arithemetic. They are ordered, and most of them are infinite. TThere is no single "infinity". There are different sizes of infinity, as with the infinity of the real numbers being larger than the infinity of the integers.

You run into the same problem there, though. There is no largest cardinal number.

The real message is that "infiinity" is somewhat subtle, and one needs to understand it or run the risk of reaching unfounded conclusions.

BTW if people would like a readable treatment of cardiinal and ordinal numbers the book Naive Set Theory by Paul Halmos is highly recommended.

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