How is 2^Aleph_0, uncountable?

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Intellectual_26

Saying 2x2x2, Aleph_0 times is as Measurable as adding 1+1+1...Aleph_0 times!

Intellectual_26

Hmmm...

I don't know if I miss the haters' comments or not!?

Lincoy3304
It’s because it’s Aleph_1. I’ll post a solution soon
Intellectual_26
Lincoy3304 wrote:
It’s because it’s Aleph_1. I’ll post a solution soon

Hmmm...No proof?

(Aleph_0)^(Aleph_0) is equal to Aleph_1 and is equivalent to ♾️^♾️ which is truly an uncountable form.

pcwildman

Define aleph. Don't hate you, it's just fun playing Devil's Advocate with the Devil's Advocado. 🐮?

Intellectual_26

Thanks for the neat off-handed compliment My Man.

This is the Best source I could find on why, Georg Cantor used the Hebrew Letter, "Aleph" to describe his "Transfinites."

https://math.stackexchange.com/questions/1635589/why-was-aleph-aleph-chosen-for-infinities

Cantor had Jewish roots, which is probably why he was familiar with the Hebrew alphabet. But it's unlikely to be the reason de jure or de facto for the choice.

From Georg Cantor: His Mathematics and Philosophy of the Infinite By Joseph Warren Dauben:

Not wishing to invent a new symbol himself, he chose the aleph, the first letter of the Hebrew alphabet. The choice was especially clever, as he was happy to admit, since the Hebrew aleph served simultaneously to represent the number one, and the transfinite numbers, as cardinal numbers, were themselves infinite unities. (p. 179)
The author then continues with something that looks like an anecdotal ex post facto explanation about how this represented a new beginning.

Intellectual_26

https://www.urbandictionary.com/define.php?term=Devil%27s%20Avocado

Devil's Avocado
 
A person who expresses a contentious opinion in order to provoke debate or test the strength of the opposing arguments.
'Just to play Devil's Avocado here, if we continue to feed the birds then they might become dependent on humans for food, and then starve when it is no longer viable for us to continue feeding them'

Intellectual_26

In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered. They were introduced by the mathematician Georg Cantor and are named after the symbol he used to denote them, the Semitic letter aleph ( ).

pcwildman

"I did not know that. Did you know that?" "Yes, oh Great One." "May a camel fall in love with your Sister's big toe."

I'll definitely have to check it out. Didn't dig deep enough to get to Cantor, but I've heard of him. Lincoy is the one who's good at this stuff. There are so many different cool areas of math to play around with. I do mostly navigation and Astronomical calcs with Spherical Trig. Keep thinking outside of the avocado. happy That was a transcriber error, and sometimes they are better than what you were saying. happy

pcwildman

Doh! I just now looked at the link. I had no idea that would be in the urban dictionary. I thought I was being clever. Same thing as devil's advocate, and I don't consider it an insult either way. It wasn't meant that way.

pcwildman

And the 2nd definition is completely out.

Intellectual_26
pcwildman wrote:

And the 2nd definition is completely out.

What 2nd definition, Sir?

pcwildman

It's unrepeatable in polite company. They'll lock you. It's horrible. We shouldn't even say anything. angry I advise you not to look it up until you are 100 years old. I wish I had waited.

We might even do good by erasing the conversation. I had no idea it would lead to this. Or maybe just edit to keep the context and eliminate the joke turned sour? No one is reading this anyway, so I think we're OK.

pcwildman

I have a vague recollection of studying this stuff way back when. Cantor rang a bell and I remember being fascinated by set theory. I'll have to do a review.

pcwildman

You know, it's hard to find a good argument anymore. Everyone always gets so mad. I love a good debate. It's how I learn. Let's pull the problem apart and look at it piece by piece and see what we can conclude. There's more power in multiple minds. Remember the Borg. They don't argue. They discuss the problems, give their input and make decisions. All within 2 milliseconds. The fighting only lasts millionths of a millisecond. We're just a bit slower. happy

Intellectual_26

wink Coool