There is no biggest number with a name.
Aleph-null is the name of the first level of infinity which is the size of a countable infinite set, ie one that can be put in a one-to-one correspondence with the counting numbers (1, 2, 3, ...., ∞).
Aleph-one is the name of a higher lever infinity.
Aleph-two is the name of an even higher level infinity
And so on.
They are useful in distinguishing the cardinality of different infinite sets.
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There is no biggest number. Numbers go on forever. Infinity isn't a number.
No. (Googolplex plus one) is bigger. As you can see, there's no such thing as a "biggest" number. No matter how big a number you name, I can always name a bigger number simply by adding '1' to yours.
1111
No. ( 1021 + 1 ) is bigger. There's no such thing as the biggest number. Whatever number you name, no matter how big it is, I can always add ' 1 ' to it and make a bigger number.
The biggest number that can be possibly be written, is 10^4*185