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Now This Just Isn't Funny

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Praefectus Praetorio said:
If we are going to wax mathematically philosophical here, it is interesting to note that modern higher math embraces all sorts of ridiculous concepts of numbers, starting with the insane, but totally indispensable square root of negative 1 (i). It is even called "imaginary! And infinity (which has no physical meaning - Sorry Buzz Lightyear!) is used regularly in simple integrals in physics! But that poor, simple number 1 divided by zero, is excluded and banished to outer darkness, allowed no meaning in math. Left to wander in perpetual ignominy.:(:(:(
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Well, the square root of -1 makes sense: it makes every polynomial of degree n have n roots. It also makes a lot of physics calculations that get verifiable results possible (so long as you throw away the "imaginary" part at the end). It also simplifies a lot of things. It's not mathematically indefensible. It just completes some things.
There are, however, other problems, like two kinds of infinities. The first is a countable infinity, that you get if you count from 1 to the end of time. (An example is "Hilbert's Hotel, which has an infinite number of rooms. There's always room for one more--every guest just moves to the next room number up and the newbie goes into room 1.) The other is an uncountable infinity, with more "members" than can be labeled with an integer (you can prove it!). The first is the rational numbers. The second is the real numbers. And, as Feynman, said, there are "more numbers than numbers": 1, 2, 3, ... has just as many members as 3,6.9.... Both are countable, and both are infinite, but somehow one is smaller than the other. Then there is Cantor's "middle thirds" set. Start with numbers 0 or greater and 1 or less. Remove all the numbers after 1/3 and before 2/3. From what is left, remove numbers greater than 1/9 and less than 2/9, and greater than 7/9 and less than 8/9. Keep going, and you get an infinite number of members which can't be matched up with the counting numbers. (This is kind of like Xeno's turtle which starts ahead of Apollo and wins the race because Apollo requires x time to make up half the distance, x/4 to cover half the remaining distance, then x/8 to cover half the remainder, etc., and never catches up. Also, there is Bertrand Russel's "set of all sets which aren't members of themselves". Is it a member of itself? If it isn't, it's in the set of all sets which aren't members of themselves and therefore is a member of itself, so it is. If it is, then it's not in the set of all sets which aren't members of itself, so it isn't.
All this bothers some people, but one book I have says "so what? it works.".
There is obviously something wrong with our heads, with how we perceive things. But then, we imagine all kinds of magic stuff that isn't real, so maybe that's not so surprising. It's a fun thing to do in retirement, I guess. It's like the lunatic in Dana Sobel's book "Longitude" who does endless longitude astronomical calculations on the asylum walls before sea captains had good clocks. Or the guy who had "A Beautiful Mind" but needed some help to get back to reality.
 
Praefectus Praetorio said:
I'm SO jealous!!!!

I don't believe in astrology, butView attachment 706610
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In 1968 a New Orleans area a 7th grade parochial school class went on a field trip to the French Quarter. There they visited a head shop. Shortly, a pre-Sexual Revolution, pre-internet porm pious altar boy saw the black light posters below.

I really didn’t understand what I was seeing. Our teacher Sister Mary Ann freaked. And no class from that parochial school ever went on a field trip to the French Quarter again. :rolleyes:
 

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Apostate said:
Our teacher Sister Mary Ann freaked. And no class from that parochial school ever went on a field trip to the French Quarter again.
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I'm not surprised. Those early unregulated black lights could cause serious damage to your eyes!
image.jpgGlad she was looking out for you!
 
The pinnacle of evolution
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Classical education
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We trust RR, don't we?
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Women and Apples, a dangerous combination!
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Frank Petrexa said:
The other is an uncountable infinity, with more "members" than can be labeled with an integer (you can prove it!). The first is the rational numbers. .
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I think that is not true. There is a numbering system which maps each rational number to an integer. Therefore there are countable infinite rational numbers.

Let's look at 1/0 . Well, what does x / y = a mean? Division is the inversion of multiplication, and x / y = a means x = a * y , and it is understood that this is a true and unequivocal statement.
Now with y = 0 you get x = 0 for every and each a, and this is neither reasonable nor unequivocal. So division by zero gives nonsense and is "forbidden"
 
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