No. Infinity is not a number.
Googol is pretty tiny as large numbers go; I can write it out in full here:
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Googolplex, defined as "ten to the power of a googol", is much larger and there isn't enough space in the entire universe to write it down in full, but it can be written down as a power tower easily; 10^(10^100). This makes it still "tiny" as far as truly large numbers go. For example, there's not enough room in the universe to express the even the first iteration (of 64) in Graham's number as a power tower; you have to invent a new system of notation to even describe it.
And even Graham's Number is infinitely small compared to infinity.
Infinity itself (of the type we're talking about here, formally called aleph-null), though it's, well, infinite, is infinitely small compared to the power of the continuum.
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