THURSDAY, NOVEMBER 17, 2022
Nova does it again: Which is larger? The number of plain old "counting numbers" (1, 2, 3, 4, 5, 6 and the like) or the number of even counting numbers (2, 4, 6 and the like)?
We're sorry to tell you that the PBS program, Nova, was noodling around with that one last night, straight outta Arsenio Hall's "Things that make you go hhhmmmm."
Here's the way it started:
TALITHIA WILLIAMS: Consider this: which is infinity is bigger? The set of counting numbers, 1, 2, 3, 4 et cetera, or the set of just the even numbers, 2, 4, 6 and so on?
EUGENIA CHENG: And intuitively we might go, “Well, that’s half of them.”
TALITHIA WILLIAMS: That’s half. Right.
The noodling continued from there, making viewers go hhhmmmm. To read the transcript or watch the tape, you can just click here.
See, you didn't have to wait long to see an example of Somerby's sexism. What makes this sexist? That it is reported with the comment "hmmmm."ReplyDelete
It reminds me of the old joke "An asshole says hmmmm? Huh?"
Well, of course you can associate every positive integer with every even integer: n*2. But then, as we seem to recall, there are infinite sets that can't be enumerated this way.
The set of all real numbers is uncountable.Delete
From Lawyers Guns and MoneyReplyDelete
When you graph the first order of difference between Republicans and Democrats an anomaly just jumps out at you. This is clearly not a random stochastic process. If it were a stochastic process you would expect the possible values which are 1, 2, 3, 4, 5, 6, to occur in more or less, similar proportions. However, you notice immediately there are no values of 5, there are no first order of different changes in the King Wen sequence of 5. Now what is the prohibition against 5 about? I don’t know but its worldwide and Neolithic. Astragali are the knucklebones of sheep that have been used since the late Neolithic inter-roman times to gamble with by burning dots into the knucklebones, and in fact playing dice is called throwing the knucklebone. There are no Neolithic astragali with 5 dots burned into them, it’s a number which is just strictly avoided. So there is some curious thing going on with the number 5, knowing that Timaeus as people are coming in and sitting down for dinner, Plato turns to Timaeus and he says “The one generates the two, and the two the three, but where oh where is the fourth my dear Timaeus.” And this the first four numbers seem to lie in a much more archetypically intense relation than the number 5.
TDH, my advice is to let this go. It doesn't go anywhereReplyDelete
Too bad he doesn’t read his comments.Delete
The set of even numbers is clearly a subset of the set of natural numbers (Somerby calls them “counting numbers.” Whatevs. )ReplyDelete
Restated: for any set of consecutive natural numbers beginning with 1 and continuing to x, there exists a subset of this set containing the even numbers within the original set. This set of even numbers is smaller than the original set (ie it has fewer elements). The proof that this is true for any finite set of appropriate natural numbers is done by induction. (It isn’t sufficient in mathematics to say “well anyone can see that it’s true.”)
This process indicates that the infinite set of natural numbers is more dense than the infinite set of even numbers. For every element in the set of even numbers, there are two elements in the set of natural numbers. Cheng and Williams have it right.
There is an obvious one-to-one correspondence between the integers and the even integers. There is no one-to-one correspondence between the integers and the reals.ReplyDelete
I would like to take part in this discussion, I think that the even numbers are larger. My sister has got a degree at Math and at one of her articles https://sway.office.com/Nk9iCyQByQEULft1?ref=Link there are some explanations in this issueReplyDelete