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The rationale escapes me. How does he figure that he would ever reach the end of integers?

More to the point, the number infinity isn't a real number, so the fact that you can double infinity and still have infinity doesn't mean your second infinity is somehow "bigger" than your first infinity, even if you have infinity times infinity to the power of infinity.

I wonder what Vi Hart would have to say about this. I'm pretty sure I've heard her say that infinity is not, in fact, a number at all, so quantifying and comparing it doesn't make sense.

Anybody?

I find the idea of multiple Vi Harts quite exciting.

>> ^HaricotVert:

Vi Hart gives me such a math hardon


She totally euler's your identity?

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Vi Hart gives me such a math hardon

>> ^kceaton1:

I could destroy her whole concept by reducing the entire mathematical world to a structure scheme that can ONLY be ever displayed as a fractional environment, except for 0 or infinity, as they are special forces unto Math.

Vi actually covers this briefly when she talks about Hyperreals. Also, you wouldn't be destroying her whole concept by reducing the mathematical world to a fractional environment, as this already exists: What you describe is the set of Rational Numbers, where all numbers can be expressed as a fraction of two integers. .999... is still describable as the series 9/10 + 9/100 + 9/1000... so the concept is still sound, and still sums to 1 (or 1/1). As an aside, 0 is a rational number and can be expressed as a fraction as well. Infinity is not a number.

Finally, in before "Now you're just nitpicking" or "You don't have to be a dick." At this level, nitpicking and checking for consistency is what Mathematics is all about, so please expect it.

>> ^kceaton1:

So I would ask her this question concerning .9999~ not equaling one. If we take two pinballs and start to count all the electrons--but, midway through we strip ONE electron from one pin; essentially making this our .9999~ pinball. By the time we get done counting the electrons which pinball will have less and which will have more? Well the problem is that IN FACT the pinball that had one taken off could actually NOW have more than the other pinball. So do either actually equal one?

There is a fundamental flaw in this reasoning, which is that the number of electrons in both pinballs is finite. You will eventually stop counting, and when you divide (electrons in Pinball A) by (electrons in Pinball B) you end up with a rational number which is not 1, but also not equal to .999..., so the test is inconclusive. Assuming both pinballs had an infinite number of electrons in them also does not help, as then the answer to "what is ePA/ePB" is "I will never stop counting" (implying correctly that Infinity - 1 = Infinity).

>> ^kceaton1:
This is why Mathematics are very specific, but in use--in the field--they will have LARGE caveats where the majority of the mental masturbation falls completely apart. Because, many of these discussions DO OCCUR at the EXTREMES of Math (if you know what I mean) and fundamentally the only places that use these parts are in extreme measurements; measurements where chance can become a powerful player.

I actually disagree with you here, though I think in practice we both have the same respect for Mathematics, so you can take or leave that disagreement as you please. In my mind Mathematics is "absolute" because it has been proven to be consistent, so the mental exercises are valid even in extreme cases. In those extreme cases sometimes things need to be added to what is already known to correctly describe what is going on or how something works, but the math that has come before is still sound. In fact, the soundness of Mathematics is the whole reason we can add onto it -- Because we know that it will not break. If it does, then we have done something wrong.

Haha, me too. She got me good

"Put two", on on both sides!!!! What do mean, "put two", on both sides???? YOU CAN'T JUST SAY, "PUT TWO", ON BOTH SIDES!!!!!1!11!oneoneone
>> ^robbersdog49:

I shouted at the screen before I got it...

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>> ^messenger:

There's some things in life like this video which you cannot enjoy as intended the first time if they're spoiled. The Crying Game is another example. Murder She Wrote is another.>> ^Yogi:
>> ^messenger:
Does nobody understand what a spoiler is?

I've got a friend who hates spoilers...then I read an article on Wired that said spoilers don't hurt and may even increase your enjoyment of a movie or show. So I hit him with a wrench over and over and over cause FUCK HIM I'LL TALK ABOUT SOMETHING THAT CAME OUT YEARS AGO AND HE SHOULD'VE WATCHED BY NOW!!!



Which is why the Crying Game sucks and Columbo is better than Murder She Wrote.

There's some things in life like this video which you cannot enjoy as intended the first time if they're spoiled. The Crying Game is another example. Murder She Wrote is another.>> ^Yogi:

>> ^messenger:
Does nobody understand what a spoiler is?

I've got a friend who hates spoilers...then I read an article on Wired that said spoilers don't hurt and may even increase your enjoyment of a movie or show. So I hit him with a wrench over and over and over cause FUCK HIM I'LL TALK ABOUT SOMETHING THAT CAME OUT YEARS AGO AND HE SHOULD'VE WATCHED BY NOW!!!

>> ^messenger:

Does nobody understand what a spoiler is?


I've got a friend who hates spoilers...then I read an article on Wired that said spoilers don't hurt and may even increase your enjoyment of a movie or show. So I hit him with a wrench over and over and over cause FUCK HIM I'LL TALK ABOUT SOMETHING THAT CAME OUT YEARS AGO AND HE SHOULD'VE WATCHED BY NOW!!!

Her explanations were correct, but less clear than in the vid you posted. I think her video style is designed to appeal to school kids mostly, but it appeals to me to. She works with children in her offline life.>> ^rottenseed:

Her math and explanations for case 1 were sloppy at best, incorrect at worst. This video is more clear.

>> ^Zawash:

>> ^kceaton1:
So I would ask her this question concerning .9999~ not equaling one. If we take two pinballs and start to count all the electrons--but, midway through we strip ONE electron from one pin; essentially making this our .9999~ pinball.
Too late, MonkeySpank already tried that one.
The number "missing", the number between .9999~ and 1, could be stated as x, where x -> 0 (x goes towards zero).


I know, but sometimes it helps people to hear the SAME explanation in none mathematical terms. That was the only reason I made it. Essentially, the number that is the difference between .999~ and 1 equaling each other eventually becomes SO SMALL that it essentially doesn't exist anymore--for all intent and purposes.

I could have have 100 pinballs and it's unlikely that they all have the same amount of atoms, let alone electrons. BUT, the point is that to me each one of those objects are still pinballs (unless we change the definition of what a pinball is, which would require superhuman measurement...).

BTW - You might think me on the wrong side of the street, maybe. To me .999~ does indeed equal 1 in every-way; how we've defined the very principles that describe so many of its different definitions are agreed upon by the very nature of the laws and mechanics that Math is built upon. I just thought it would be fun to play around with the definitions a bit and see that we still end up at the same place. Math describes something intrinsic about the nature of the Universe and reality.

>> ^kceaton1:

So I would ask her this question concerning .9999~ not equaling one. If we take two pinballs and start to count all the electrons--but, midway through we strip ONE electron from one pin; essentially making this our .9999~ pinball.
Too late, MonkeySpank already tried that one.

The number "missing", the number between .9999~ and 1, could be stated as x, where x -> 0 (x goes towards zero).