How big is infinity? - Dennis Wildfogel

View full lesson: http://ed.ted.com/lessons/how-big-is-...

Using the fundamentals of set theory, explore the mind-bending concept of the "infinity of infinities" -- and how it led mathematicians to conclude that math itself contains unanswerable questions.

Lesson by Dennis Wildfogel, animation by Augenblick Studios.

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[ThinkTank255]

"God" is supposedly "infinite", so "God" does not exist either. I mean, clearly finite "God" really is not a "God" at all. So, the universe is finite AND there is no "God". Both are logically derivable consequences of the nonexistence of infinity.

[ThinkTank255]

"'God' invented the universe and physics"

That is absurd, if the universe did not exist then no "inventing" could take place. You hold a childish and simplistic view of the universe (along with 85% of the rest of humanity). That we invented a word is not surprising. Who else would have invented it??? Your imaginary "God"??? LOL. Whether or not that word has meaning is a completely different matter. Being able to utter a word does not make it meaningful.

[ThinkTank255]

Frankly, you are confused because you have accepted the insane "axiom of infinity", which itself relies on inductive sets, which are circularly defined. It is a gaping hole in mathematics.

What is strange is that Hilbert and his group won the battle against infinity quite a while back, but everybody nowadays seems to forget that.

"You just need a rule, describing ..."

What exactly do you think an algorithm is? It is a set of rules that describe things.

[cavello89]

Whoa. These are the kind of vids that make me doubt my intelligence -.-

[amatysten]

"IF both sets (naturals and reals) exist, then every element of both sets must be identifiable by non-terminating algorithms" -- wrong. You just need a rule, describing it's elements collectively, not a linear algorithm.

[amatysten]

It's difficult to come up with a difinition of more or less or equal when you talk about infinity. A good one (arguably the only sensible) is: if you can map numbers from set A to set B but not vice versa, then set B is larger.

If you accept that difinition then clearly there're more irrational numbers than whole ones. If you don't accept then you're in trouble, because everyone does and you'll have to develope your own theories from scratch. Math have nothing to do with agree-disagree.

[CallTheWaambulance]

I disagree with this video's theory. You can't have "more of infinity". It's simply more detailed numbers.

For example, there are infinite decimal numbers and infinite irrational numbers. Because an irrational number has a decimal place, it allows as decimal numbers to be appended to itself. This is still infinite, something which you can not have "more of".

[CallTheWaambulance]

Wrong.