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5150 clicks; posted to Geek » on 10 Feb 2014 at 2:44 PM (3 years ago)   |   Favorite    |   share:    more»

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Can you prove that someone actually got paid to write that 'article'?

There's more than one infinity

Math

Can't live with it
Can't live without it.

DammitIForgotMyLogin: There's more than one infinity

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

I just finished Calc II (first try) last semester. That series is non convergent, next question.

Talondel: DammitIForgotMyLogin: There's more than one infinity

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

There are an infinite number of integers, and there are an infinite number of even integers, but there are twice as many even integers as integers.

DammitIForgotMyLogin: There's more than one infinity

and some of them are bigger than others...

Talondel: DammitIForgotMyLogin: There's more than one infinity

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

infinity/2 = infinity

infinity + 8 = infinity

infinity - infinity = infinity

Infinity is just math telling you that you goofed.

DammitIForgotMyLogin: There's more than one infinity

Semantics: there is more than one infinite set of numbers. IMO, "real" infinity, true limitlessness, cannot be defined.

CREATIONIST-LIKE TYPING DETECTED.

As a mathematician, I say go fark yourself,  subby.

So the next time I suggest a threesome, my finishing argument should be "because math"?

jigger: DammitIForgotMyLogin: There's more than one infinity

Semantics: there is more than one infinite set of numbers. IMO, "real" infinity, true limitlessness, cannot be defined.

This is why I am anti-semantic.

How many mathematicians doesn't it take to screw in a lightbulb?

moos: DammitIForgotMyLogin: There's more than one infinity

and some of them are bigger than others...

All infinities are equal, but some are more infinite than others.

Talondel: DammitIForgotMyLogin: There's more than one infinity

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

The size of the set of real Numbers is the same as the power set of Rational/Integer/Natural Numbers.
// Use to know the proof, but have not read it in like 10 years.

DammitIForgotMyLogin: There are an infinite number of integers, and there are an infinite number of even integers, but there are twice as many even integers as integers.

does not work, since there is a 1-1 mapping between the set of  Integers and the set of Even Integers, which is only possible because the set is of infinite size,
there is also a 1-1 mapping between Integers and Rational numbers (like 1/4).

cgraves67: moos: DammitIForgotMyLogin: There's more than one infinity

and some of them are bigger than others...

All infinities are equal, but some are more infinite than others.

Some girls are bigger than others
Some girls' mothers are bigger than other girls' mothers...

Talondel: DammitIForgotMyLogin: There's more than one infinity

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

Easy way to prove it:
There are an infinite ammount of numbers between 1 and 2.

None of those numbers are 3. And none of those numbers contain any of the infinite numbers between 2 and 3.

100 = 1

100 =   i 4

100/2 =  i 4/2

100 =  i 2

1 = -1

Q.E.D.

The only way to get M=-1 is to drop the last term, so instead of being 1+1+1+...
it becomes -1 + infinity-infinity, where you pulled a sleight of hand by adding "- infinity". So the sums are different.

For the first one, it's an alternating sum, so N even n.e. N odd.

/ not a mathematician, but I think there are better examples.

idsfa: 100 = 1

100 =   i 4

100/2 =  i 4/2

100 =  i 2

1 = -1

Q.E.D.

Breaks the rules of complex numbers.

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

There are an infinite number of integers, and there are an infinite number of even integers, but there are twice as many even integers as integers.

False. When it comes to infinity, you can't really say "as many [...] as", but there is a notion of countably infinite. Your example fails, because you can perfectly match up the integers with the even integers. Just match 0-0, 1-2, 2-4, 3-6, 4-8... and all the negatives as well. Perfect match. Every integer has a unique even integer cousin, and vice versa.
Now, the real numbers, that's the sumbiatch that gets you.

sjmcc13: The size of the set of real Numbers is the same as the power set of Rational/Integer/Natural Numbers.
// Use to know the proof, but have not read it in like 10 years.

here, let me Google that for us:

http://en.wikipedia.org/wiki/Cardinality_of_the_continuum

idsfa: 100 = 1

100 =   i 4

100/2 =  i 4/2

100 =  i 2

1 = -1

Q.E.D.

Square Roots do not work like that.

Felgraf: Talondel: DammitIForgotMyLogin: There's more than one infinity

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

Easy way to prove it:
There are an infinite ammount of numbers between 1 and 2.

None of those numbers are 3. And none of those numbers contain any of the infinite numbers between 2 and 3.

Not nearly sufficient as a proof. You need to guarantee that you can't matchup one of the numbers between 1 and 2 with 3; another such number with 4; another such number with 5; and in doing so assign each real number between 1 and 2 with an integer. The proof that you can't is a little tricky.

The Abbott & Costello versions are good too.

/numberphile on youtube has a few different brain melting maths too

(-1 + 2) + (-2 + 3) = 2
-1 + (-1 +1) + (-2 + 2) = -1

There's no distributive property for addition.

moos: DammitIForgotMyLogin: There's more than one infinity

and some of them are bigger than others...

Darn you!  Well-played, but darn you all the same.

/loved the bit about not eating breakfast before 6:00 'because I'm not a Russian peasant fortifying myself for a day in the fields'

1  =  i 4

log 1 = log  i 4

0  = 4 log  i

0  =  log  i

100  =  10log  i

1 =  i

12 =  i 2

1 = -1

Q.E.D.

idsfa: 1  =  i 4

log 1 = log  i 4

0  = 4 log  i

0  =  log  i

100  =  10log  i

1 =  i

12 =  i 2

1 = -1

Q.E.D.

Still breaks the rules of complex numbers.

Talondel: DammitIForgotMyLogin: There's more than one infinity

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

Somebody or other's diagonalization (I wanna say Cantor, but I'm too lazy to check).

Basically:

write down all the integers in a column
For each integer, write down a real number next to it.

Now -- the diagonalization:  Take the real number in the first row, and change its first digit.
Take the real number in the second row, and change its second digit.
...
Take the real number in the n'th row, and change it's n'th digit.

You've just constructed a real number that can't be counted by the integers.  Have a beer.

segmentation fault

idsfa: 0  =  log  i

Nope.  log(i 4) = 0 though (only because i 4 = 1), so you were okay up to that point...

i is not a variable, and there are special rules for dealing with it.
=Smidge=

God

Sliding Carp: Talondel: DammitIForgotMyLogin: There's more than one infinity

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

Somebody or other's diagonalization (I wanna say Cantor, but I'm too lazy to check).

Basically:

write down all the integers in a column
For each integer, write down a real number next to it.

Now -- the diagonalization:  Take the real number in the first row, and change its first digit.
Take the real number in the second row, and change its second digit.
...
Take the real number in the n'th row, and change it's n'th digit.

You've just constructed a real number that can't be counted by the integers.  Have a beer.

FIFTEEEEEEEEEEN. Yep, that is exactly it (and yes, it is Cantor's diagonalization argument).

(-1 + 2) + (-2 + 3) = 2
-1 + (-1 +1) + (-2 + 2) = -1

There's no distributive property for addition.

I don't know what argument you're trying to make, but what they're using in those lines is the associative property, which is totally kosher (for finite sums). For infinite sums, you get that farkery. I thought we covered this last month with the farking -1/12 bullshiat.

RminusQ: Sliding Carp: Talondel: DammitIForgotMyLogin: There's more than one infinity

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

Somebody or other's diagonalization (I wanna say Cantor, but I'm too lazy to check).

Basically:

write down all the integers in a column
For each integer, write down a real number next to it.

Now -- the diagonalization:  Take the real number in the first row, and change its first digit.
Take the real number in the second row, and change its second digit.
...
Take the real number in the n'th row, and change it's n'th digit.

You've just constructed a real number that can't be counted by the integers.  Have a beer.

FIFTEEEEEEEEEEN. Yep, that is exactly it (and yes, it is Cantor's diagonalization argument).

Yay!  I did look it up after I wrote that, in case I had to apologize.  And I should have said 'natural numbers' instead
of 'integers', and specified all the real numbers you write down should be unique (like that's hard -- just stick a '.0' on its index).

So are the integers bigger than the natural numbers?  I'm guessing no, but I'm no mathematician.  I'm also guessing that using integers in that argument gets real funky with the negative numbers, but that's just a guess.

And thanks for what you're doing.  It's nice to be reminded that there are still kids who care about learning, and know that math is fundamental with a capital fun.

idsfa: 1  =  i 4

log 1 = log  i 4

0  = 4 log  i

0  =  log  i

100  =  10log  i

1 =  i

12 =  i 2

1 = -1

Q.E.D.

No. Not even close

Article:

"This set is non-convergant, which means its sum cannot equal an integer.

"Let's set the sum equal to the integer N."

Sliding Carp: RminusQ: Sliding Carp: Talondel: DammitIForgotMyLogin: There's more than one infinity

Yes, and I used to know how to prove it, but can't recall now.  Something to do with not being able to count all the numbers in the set (Real) with any number of sets of (Rational).

Somebody or other's diagonalization (I wanna say Cantor, but I'm too lazy to check).

Basically:

write down all the integers in a column
For each integer, write down a real number next to it.

Now -- the diagonalization:  Take the real number in the first row, and change its first digit.
Take the real number in the second row, and change its second digit.
...
Take the real number in the n'th row, and change it's n'th digit.

You've just constructed a real number that can't be counted by the integers.  Have a beer.

FIFTEEEEEEEEEEN. Yep, that is exactly it (and yes, it is Cantor's diagonalization argument).

Yay!  I did look it up after I wrote that, in case I had to apologize.  And I should have said 'natural numbers' instead
of 'integers', and specified all the real numbers you write down should be unique (like that's hard -- just stick a '.0' on its index).

So are the integers bigger than the natural numbers?  I'm guessing no, but I'm no mathematician.  I'm also guessing that using integers in that argument gets real funky with the negative numbers, but that's just a guess.

And thanks for what you're doing.  It's nice to be reminded that there are still kids who care about learning, and know that math is fundamental with a capital fun.

Read that in Professer Ethan 'Bubblegum' Tate's voice

/on my iThing, so no image :(

Bareefer Obonghit: Can you prove that someone actually got paid to write that 'article'?

Yeah, 1+1-1+1-1+1-1+1-1 Is NOT the same as (1-1)+(1-1)+(1-1). it's not like they just added parentheses and called it good. WTF WAS that shiate?

blacksharpiemarker: How many mathematicians doesn't it take to screw in a lightbulb?

I want to know how they got inside the lightbulb in the first place.

Bareefer Obonghit: Can you prove that someone actually got paid to write that 'article'?

This is as stupid as the "Can't get pregnant from a gun bullet" story from this weekend that didn't "prove" anything except that the original story was faked. "Proof" means showing that it couldn't happen, not that someone made up the original story in the first place, I was expecting some kind of science and test results.

I was told there would be no math!

In this way, we've "proved" M is equal to infinity and M is equal to negative one. So negative one is equal to infinity. Meaning you only have to go slightly into debt to have an infinite amount of money.

A guy that had a dog with a bad leg he named Arithmetic.

Because he out down 3 and carried the 1.

Tommy Moo: Article:

"This set is non-convergant, which means its sum cannot equal an integer.

"Let's set the sum equal to the integer N."

This.

I was all set to write an indignant critique, and you summed it all up in just two sentences. Nice.

/I'm just a statistician, not a mathematician. We don't do infinite series; we just use the first couple of terms and say 'close enough' (mostly the first two terms of the Taylor series).

Robin Hoodie: FARK MATH THREAD EVERYBODY RUN!!!!

1=.999...

Goddammit people, the definition of an infinite series is the limit of its partial sums.

Unless you respect that definition, everything you're doing is farking meaningless.

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