The Continuum Hypothesis claims that

There is no set whose cardinality is strictly between that of integers and real numbers.

I went out on an adventure checking what people think about it.

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TopNewest@John Muradeli : What do you think about this? – Agnishom Chattopadhyay · 2 years, 5 months ago

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lolz I have no idea as far as the answer to that question goes, but great job trolling those cyborg representatives! cyborg cause if you look how similar their responses are, you'll see they mostly follow a script - or, a program ;)

Now if I knew what the heck a cardinal is, I might have a better idea. But I'll tell you one thing:

If a solution to that problem exists, I don't have an answer. If a solution to that problem doesn't exist, I have the answer. – John Muradeli · 2 years, 5 months ago

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Cardinality of a set is loosely defined as the number of elements in that set. E.g, Cardinality({Calvin, Sue, Pete, Arron})=4

The cardinality of the set of real numbers is higher than the set of natural numbers, as you might notice, even though they are both infinite.

The question is if there is any set whose cardinality is between these two.

Well, if you have any chatroom transcripts, please share them. – Agnishom Chattopadhyay · 2 years, 5 months ago

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The complex integer set? Integers with complex interger combos.

The whole number set? Includes zero.

The rational number set? Real minus irrational.

The irrational number set? Real minus rational. – John Muradeli · 2 years, 5 months ago

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We say that two sets are of the same cardinality if there is a bijection, i.e, an way to associate all elements of one set with all elements of the other.

For example, {Red, Green Blue} and {A,B,C} are of the same cardinality because we may establish a bijection like this:

A -> Green, B -> Blue, C -> Red

That is why we can say that the number of elements in set 1 = number of elements in set 2 or their cardinalities are equal.

It can be shown that there are as many integers as rational numbers or natural numbers by establishing a bijection between them. – Agnishom Chattopadhyay · 2 years, 5 months ago

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I've seen on YouTube though how the number of real numbers between 0 and 1 is greater than the number of Natural numbers due to some weird property that lets you invent more numbers than natural ones allow or some weird stuff like that...

But alright what about, at least, complex integer set? It's like complex natural numbers and their negative counterparts (and zero!). Can you "show" that too?

Anyway, I hold the answer to your question, like I said. If a condition applies... – John Muradeli · 2 years, 5 months ago

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Post 7 in this thread – Agnishom Chattopadhyay · 2 years, 5 months ago

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Sorry :p – John Muradeli · 2 years, 5 months ago

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Check that link – Agnishom Chattopadhyay · 2 years, 5 months ago

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Importantlist for the next week (got hw from 7AP classes as of now).Thanks! – John Muradeli · 2 years, 5 months ago

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– Agnishom Chattopadhyay · 2 years, 5 months ago

Hahaha... LOLLog in to reply

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reference – Agnishom Chattopadhyay · 2 years, 5 months ago

Mandatory xkcdLog in to reply

– John Muradeli · 2 years, 5 months ago

You made that website, didn't you? ;pLog in to reply

– Agnishom Chattopadhyay · 2 years, 5 months ago

No. xkcd is an webcomic by the great Randall MunroeLog in to reply

Dude, this made my day, I read this when just woke up and I believe that this was the first time I didn't sleep through a morning chem lecture. – Trevor Arashiro · 2 years, 5 months ago

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– Agnishom Chattopadhyay · 2 years, 5 months ago

Glad that you like itLog in to reply

WOW!!! Troll of the millennium, I wish I were there in place of those ppl you trrolled, wanna find how it feels to be trolled, @Agnishom Chattopadhyay – Satvik Golechha · 2 years, 5 months ago

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@Agnishom Chattopadhyay , it appears that you've made a typo in the statement of the continuum hypothesis. – Mursalin Habib · 2 years, 5 months ago

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– Agnishom Chattopadhyay · 2 years, 5 months ago

Yup, fixed it. Thanks :)Log in to reply

Have u really chatted with them? @Agnishom Chattopadhyay – Ravi Dwivedi · 1 year, 5 months ago

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– Agnishom Chattopadhyay · 1 year, 5 months ago

Yes. Please don't let them know it was meLog in to reply

– Ravi Dwivedi · 1 year, 5 months ago

Why u did that??any purpose in mind??Log in to reply

– Agnishom Chattopadhyay · 1 year, 5 months ago

Not reallyLog in to reply

Thank you for helping me with the code, Agnishom :) – John Muradeli · 2 years, 5 months ago

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– Agnishom Chattopadhyay · 2 years, 5 months ago

Mention notLog in to reply