TML: The Infinities In Between (2 of 2)

more on infinity and the Continuum Hypothesis

Category:

Education

Tags:

• continuum
• hypothesis
• Cantor
• infinity
• Set
• Theory

[kaosmostly]

Great video.

And super groovy music at the end.

Is it you playing?

If so, you should call your band Aleph and the Infinities.

If it's not you, tell us where to find more of this music.

Thanks

[CellarAcademic]

@kaosmostly If I create a band, I'll use that name and give you credit. The song in the vid is called "Soul Thing" by Tony Newman

[DanRYoung]

You've presented a very clear video examining some of the astounding ideas Cantor gave us. I have yet to take a class on set theory, but your video is good inspiration to consider doing so. Thanks!

[CellarAcademic]

Thanks much. Be warned however. Set theory can be mind-numbing. It's essentially 90% philosophy (the scary kind of philosophy).

[owchywawa]

Why wouldn't someone assume that all numbers are infinite; that all numbers are actually subsets of infinity? There are infinite points between the numbers 1 and 2 for example. Would not then 2 simply be a set of infinity?

[CellarAcademic]

You could do that if you found something useful in the process. Of course, in that case, it would be difficult to call it math since the number 2 has had a very simple, concrete, and finite interpretation ever since humans were counting their sheep

[hmodywakid]

number 8 in 0:35 is wrong it should be phi not {phi}

[siddisidam]

@CellarAcademic Yeah....this is actually the hidden dimension of every day numbers.

Numbers look simple but hold oceans beneath them. Simple logic such as "every number whose digits add to a total of 9 is divisible by 9", and many more are not just mathematical principles. They show the extreme networking of nature and its foundation. Also, a step towards the grand unification theory.

[thewiffenpoof]

I think there's a slight inaccuracy here. The continuum hypothesis is that the cardinality of c = aleph1. Aleph1 is an ordinal and mathematicians are not sure how big it is (whether or not it is equal in size to the continuum). So you are correct that the power set of N is the continuum or 2^aleph0 but it is an open question (in fact the continuum hypothesis) whether or not 2^aleph0 = aleph1. Aleph1 is just the next larger (ordinal) cardinal infinity whatever that is.

[2eelShmeal]

I would think that there are an infinite # of infinities between the alephs. I guess the question is how you show that mathematically.

Whaddaya think? Please forgive my ignorance on the subject...

I just feel that fractal geometry will be key to explain it perhaps. How far out in left field am I?

[Arlesterc]

Excellent. I would be very interested in seeing you 'explain' Godel's theory - I haven't seen one yet and I've looked for a while.. If you have already done that/or know of one you could recommend I would appreciate a link to it.

[ILoveYouToThe9999999]

No but it needs to be proved.

[DJFishlips]

let me guess: this margin is too small to contain it :)

[gen6k]

why dont u just do an inverted power set thats a vacuum between the two but have antinumbers instead of reals.