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What is Aleph Googol?

Welcome to this blog. I'm not sure how to make a landing page explaining what this site is about, and perhaps that's a good thing. What this site is about now might not be what it will be about next year, which might not be what it's about the following year. Etc...

Let me at least explain a little about the title. Aleph Googol is an infinite number. Does that mean it's infinity? No. It's just one of the infinite numbers that mathematicians have been studying for well over a hundred years now.

It's written: \( \aleph_{10^{100}} \), and represents the \(10^{100}+1 \)-st infinite cardinal. Why the \(+1\)? Because infinite cardinals start with \(\aleph_0\), making \(\aleph_1\) the second infinite cardinal.

Will this blog actually cover much more of this material? I'm not sure.

Comments

  1. some random brainy guyApril 7, 2021 at 10:22 PM

    It really don't matter how big the number is, none of it comes close to the one and only "biggest" number: ABSOLUTE INFINITY.

    This number in mind is so big, that not even the word "big" is even relevant anymore, it is a meaningless concept. The old "sideways 8" beats em all, because it is the largest, yet smallest number in the universe and beyond. You could take a googolplexianth, multiply it by Graham's number, and then exponentiate it like (x^9999^9999^9999^9999^9999^9999^9999^9999^9999), and it STILL wouldn't even matter: it would still leave Absolute Infinity as the answer.

    To recap: AbsInf is so massive that no "aleph" number, no matter if it's aleph-null, aleph-googolplex, or aleph-aleph-googolplexianth times 2, no matter WHAT number you drum up, AbsInf will still be bigger than cardinal or aleph numbers. Adding, dividing, multiplying, exponentiating, cubing, etc. will still leave the same number.

    I guess the old sideways peanut wins yet again...

    ReplyDelete
    Replies
    1. some random brainy guyApril 7, 2021 at 10:26 PM

      (sorry I replied to my own comment, I didn't finish)

      And yet, it is also the smallest, because there is an AbsInf value worth of numbers between 0 and 1, 1 and 2, and further beyond. AbsInf is not just the BIGGEST number ever, it is also the SMALLEST.

      AbsInf can actually be found on a regular basis, when you use basic math, such as a preschooler counting 1 + 1. It's still an AbsInf amount of numbers between 1 and 2.

      And using decimals and fractions is the same.

      OOF, that's some stuff to think about. Good luck sleeping tonight!

      Delete

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