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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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Q: What is the biggest number with a name and why is it useful?
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