Is infinity squared larger than infinity?

I am right!
No I am right!
I am right times infinity!
No, I am right infinity times infinity!

When I was a child, my late brother, Sam, and I had many arguments.  One that stood out was the largest known animal.  I was big supporter of marine animals and he was a die-hard dinosaur fan.  He said Seismosaurus.  I said the Blue Whale.  We got into an argument, and infinity times infinity came up.

This is puzzling, because infinity is supposed to be "infinite" after all, but can infinity be manipulated in quantity, say only all odds, or evens, or multiplying infinity by itself?  I was reading about a mathematician that came up with some interesting ideas about the different quantities of infinity.  He considered adding a decimal to every number and  then having infinite decimal places for each number.  I read that he ended his life in an insane asylum.  Some say that it was due to his deep ponderings of infinity and some say it was more because of how many of his ideas were poorly received in his time.

Some mathematicians refused to accept infinity.  They say it does not exist.  The universe is finite and infinity is just something dreamed up in our heads, but is it really?

Most cosmologists accept the idea of inflation, that the universe blew up much like a balloon after the Big Bang.  This inflation occurs faster than light speed.  So space-time is expanding faster than we could ever travel  to find its edge.  This would mean to me that like Schrodinger's cat, infinity would both exist and not exist at the same time.  Since no matter how far you traveled there would always be more space in "front" of you, but at the same time the expansion is just occurring faster than the cosmic speed limit, so it is finite?  Right?  I don't know, just a thought.  I have considered that the physical "reality" that we perceive actually has the same properties of quantum mechanics, and the infinity idea is one example.

Many theorists think that if you reached the "edge" of the universe that it would just loop back on itself.  This would mean that if you were able to take a wormhole across the universe, you could end up standing behind yourself watching yourself enter the wormhole.  Very interesting.

Another big theory being thrown around of the multiverses: one is that there are infinite universes, meaning that also that there would be infinite versions of yourself in these other multiverses.  I was thinking of developing a way to escape our little version of reality to see what else is out there.  Then I realized that if the math was right about the infinite copies of me, as I am travelling to the other multiverses, I would then run into infinite Mes making their own little escapes from their realities.  What would this mean?  What would be the consequences, if any, to this sort of infinite encounter?  Would our little universe be destroyed due to the overload of matter caused by the infinite Mes? And would all of their universes also suffer a similar fate?  Well if the universe we experience is finite, then surely infinite copies of me would be too much for it, but if it is expanding faster than it is filling up, perhaps our universe would be ok, and maybe we would all just switch places in each universe/multiverse ensuring each ones sustainment.  I could continue on with this rambling, but I will leave that for a later blog.    There is much to be said about infinity, apparently.