How big is infinity? Seems like a rhetorical question, right? Everyone knows infinity is infinite, but leave it to the folks at TED to tackle discussing the ins and outs of what this means.
Dennis Wildfogel, according to the presentation description, “[uses] the fundamentals of set theory [to] explore the mind-bending concept of the ‘infinity of infinities’ — and how it led mathematicians to conclude that math itself contains unanswerable questions.”
Wildfogel first discusses how matching a fundamental method of thinking about a quantity without really counting. He offers the example of a packed auditorium to illustrate this point — the number of people sitting matches the number of chairs set out.
“What we mean when we say two sets are the same size is that the elements of them can be matched up one by one in some way,” he said, getting to the point that there are as many even numbers as there are whole numbers.
Continuing, Wildfogel points out “what still bothers us is our distress over the fact that the even numbers only seem to be part of the whole numbers.” He then starts talking about making a list of all the fractions, shows how the fractions match up with the whole numbers, brings up rational and irrational numbers . . . and then we start getting lost in our after lunch food coma.
As Gizmodo puts it, this discussion will either “make you smarter” or “infinitely frustration.” Check it out to see which camp you fall into: