Continuum Hypothesis - What Amazon, Samsung, Boost and the Common Man thinks about it

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.

Samsung

Imgur Imgur

Large version here

Cryptocat Lobby

Imgur Imgur

Amazon

Imgur Imgur

Large version here

Boost

Imgur

Large version here

Imgur

Large version here

#Combinatorics #Infinity #JustForFun #Troll #ContinuumHypothesis

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@John Muradeli : What do you think about this?

Agnishom Chattopadhyay - 6 years, 7 months ago

LOOL AGNISHOM THIS @$*! IS HILLARIOUS!! I just read the whole thing - and I thought I was the only one going crazy in customer support chatrooms xDD

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 M. - 6 years, 7 months ago

Well, this problem is called Continuum Hypothesis. You may look it up on wikipedia.

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 - 6 years, 7 months ago

@Agnishom Chattopadhyay – The integer set? In a sense has twice as many cardinals and includes zero, too.

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 M. - 6 years, 7 months ago

@John M. – Please do not infer the word cardinal in that sense.

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 - 6 years, 7 months ago

@Agnishom Chattopadhyay – Can it, really? Then why can't it be shown that there's as many real numbers as natural numbers?

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 M. - 6 years, 7 months ago

@John M. – What is the answer?

Post 7 in this thread

Agnishom Chattopadhyay - 6 years, 7 months ago

@Agnishom Chattopadhyay – Nvm I have no idea what the answer is.

Sorry :p

John M. - 6 years, 7 months ago

@John M. – LOL.

Check that link

Agnishom Chattopadhyay - 6 years, 7 months ago

Hm. Looks interesting. I'll add it to my Important list for the next week (got hw from 7AP classes as of now).

Thanks!

John M. - 6 years, 7 months ago

Hahaha... LOL

Agnishom Chattopadhyay - 6 years, 7 months ago

@Agnishom Chattopadhyay , it appears that you've made a typo in the statement of the continuum hypothesis.

Mursalin Habib - 6 years, 7 months ago

Yup, fixed it. Thanks :)

Agnishom Chattopadhyay - 6 years, 7 months ago

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 - 6 years, 7 months ago

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 - 6 years, 7 months ago

Glad that you like it

Agnishom Chattopadhyay - 6 years, 7 months ago

Thank you for helping me with the code, Agnishom :)

John M. - 6 years, 7 months ago

Mention not

Agnishom Chattopadhyay - 6 years, 7 months ago

Have u really chatted with them? @Agnishom Chattopadhyay

Ravi Dwivedi - 5 years, 8 months ago

Yes. Please don't let them know it was me

Agnishom Chattopadhyay - 5 years, 8 months ago

Why u did that??any purpose in mind??

Ravi Dwivedi - 5 years, 8 months ago

@Ravi Dwivedi – Not really

Agnishom Chattopadhyay - 5 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$