The Auryn is an ouroboros which is another sign for Infinity.

- spidey

hmmm... not quite the rigorous mathematical solution I was searching for. But what the hell Step up and receive your inaugural Roy Ayers Award for Sun Ra ish Cosmic Deepness

The Auryn is an ouroboros which is another sign for Infinity.

- spidey

hmmm... not quite the rigorous mathematical solution I was searching for. But what the hell Step up and receive your inaugural Roy Ayers Award for Sun Ra ish Cosmic Deepness

Dee Dee Ramone took an infinite amount of drugs and now he's infinitely dead. I'm thinking this is a little too hard to hit an 11 year old with, but life's hard lessons are coming at some point, may as well be at 11.

So now I got home, told him this and he's been on the web googling images of DeeDee's, Joey's and Johnny's graves. And let me tell you, Johhny's memorial ROCKS big time.

Jesus Christ, they buried Johnny in Boca? That's fucked up.

My 11 yr old son, mildly Apserger syndromic, posed the following to me at the weekend:

Infinity + 1 = Infinity Deducting Infinity from both sides + 1 = 0

I need to hit him with a one line rebuttal or we'll be discussing it for a year. And there are better things to talk about.

I am fast coming to the conclusion that Infinity does not exist in any meaningful way.

BTW he rides hard for the Ramones and punk in general. Any help you could give, with a punk slant, would be highly appreciated by me.

I am not holding out any hope on this one.....

There are various ways to put some meaning to "infinity" mathematically, and depending on that meaning, you get various types of infinity.

One way is to talk about "cardinal numbers" which just takes a set, say {a,b,c}, and assign the number "3" to any set which can be put into one-to-one correspondence with this set. So the set {1,2,3} has cardinality 3 since 1 --> a 2 --> b 3 --> c is a one-to-one correspondence of {1,2,3} with {a,b,c}.

Now, the first set one might think of as being infinite is the set of all positive integers, {1,2,3,4,5,...}. So, let's call every set that is in one-to-one correspondence with this set as "infinite" (this cardinal number is actually called "aleph-0", as in the Hebrew letter aleph). Then the set of all even positive numbers {2,4,6,8,...} is has the same infinite cardinality since 1 --> 2 2 --> 4 n --> 2n gives a general one-to-one correspondence between {1,2,3,4,...} and {2,4,6,8,...}.

Now consider the set of all strings of 1's and 0's that are this kind of"infinite". So, 1111111...., the string of all 1's is one of these, or 101010101010... of alternating 1's and 0's is one of these. Around 1900, Cantor proved that the set of all such strings is a different kind of infinity than the set {1,2,3,...}. That is, there is no one-to-one correspondence between the set {1,2,3,...} and the set of all such strings. The proof is by "contradiction". That is, suppose these are the same type of infinity, so that we do have a correspondence. That means we can list the strings in some order, with some string being first, another being second, and so on. The idea is to find a string that cannot be in this list no matter what the list is. If the list is something like 110010100... 001001010... 110010100... 111100111... and so on, then consider the string 0110.., which we make by changing the first digit of the first string, the second digit of the second string, third digit of the third string, and so on. So, just go down the diagonal and switch 0's to 1's and 1's to 0's. Doing this, no matter what list we have, this always gives a string not in the list, since it will differ from every single other string by at least one digit.

Cantor went crazy when he discovered this, and spent the rest of his life in a mental hospital.

But there are other ways to look at infinities. There's a great book called "Surreal numbers" by Donald Knuth that constructs another kind of infinities. But one thing you can say about the argument that 0=1 is that the mistake is that infinity-infinity is not necessarily 0. In the infinity above, infinity-infinity can be infinity, since if you take the set {2,4,6,8,...} away from the set {1,2,3,4,...}, you are left with {1,3,5,7,...}, which is still infinite.

Cantor went crazy when he discovered this, and spent the rest of his life in a mental hospital.

I don't think this is true. He developed the Cantor set after doing that and the Cantor set is not something a crazy man could construct.

I am an authority on math. Herein lies the problem with your sons deduction. The following operations are well-defined when dealing with infinity in real analysis:

1 + infinity = infinity 1 / infinity = 0

The following operations are NOT well-defined when dealing with infinity in real analysis:

0 * infinity = not defined infinity - infinity = not defined

As you can see he was wrong in stating "infinity - infinity = 0" when in fact "infinity - infinity" is not defined at all.

The most startling conclusion when dealing with infinities is the following. We can define a "countable" set of numbers as a set that can be indexed by the natural numbers. Examples are the natural numbers, the even numbers, the odd numbers, the integers, etc. However, it can be shown that the rational numbers are countable.

And since the union of a countable set and a countable set is still a countable set, in combination with the fact that the real numbers is the union of the rational numbers and the irrational numbers and is in fact, uncountable... this means that there are MORE irrational numbers than rational numbers.

Cantor went crazy when he discovered this, and spent the rest of his life in a mental hospital.

I don't think this is true. He developed the Cantor set after doing that and the Cantor set is not something a crazy man could construct.

I don't know, it seems exactly the type of thing a crazy man could construct.

I know he, at some point, spent the rest of his life in a mental institution. Not sure of the dates.

Also, subtraction can be well-defined on infinite cardinals (as long as the first is at least as big as the second). In that case, an infinite cardinal minus an equal or smaller infinite cardinal is defined to be the first larger or equal cardinal.

In the realm of surreal numbers, all kinds of operations on infinities is defined, even calculus.

no your totally right, but in application its best to think of infinity as some ridiculously large number. (aka my electrophysics class sucks nuts right now).

ABSOLUTELY WRONG. There is no point at which the very large begins to merge with the infinite. A trillion is no closer to the infinite than the number 7. Infinite classess need to be treated differently to finite classes and treating the infinite as just a very big number will inevitably lead you to error

Skel tell your 11 year old son that he is a dumbass who is not on dolo's level.

I like how those math dudes can get all deep with numbers, but still need a liberal arts major to look shit up on Wikipedia for them:

Cantor suffered his first known bout of depression in 1884.[20] Criticism of his work weighed on his mind: every one of the fifty-two letters he wrote to Mittag-Leffler in 1884 attacked Kronecker. A passage from one of these letters is revealing of the damage to Cantor's self-confidence:

"???I don't know when I shall return to the continuation of my scientific work. At the moment I can do absolutely nothing with it, and limit myself to the most necessary duty of my lectures; how much happier I would be to be scientifically active, if only I had the necessary mental freshness."[21] ???

This emotional crisis led him to apply to lecture on philosophy rather than mathematics. He also began an intense study of Elizabethan literature in an attempt to prove that Francis Bacon wrote the plays attributed to Shakespeare (see Shakespearean authorship question); this ultimately resulted in two pamphlets, published in 1896 and 1897.[22]

Cantor recovered soon thereafter, and subsequently made further important contributions, including his famous diagonal argument and theorem. However, he never again attained the high level of his remarkable papers of 1874???1884. He eventually sought a reconciliation with Kronecker, which Kronecker graciously accepted. Nevertheless, the philosophical disagreements and difficulties dividing them persisted. It was once thought that Cantor's recurring bouts of depression were triggered by the opposition his work met at the hands of Kronecker.[9] While Cantor's mathematical worries and his difficulties dealing with certain people were greatly magnified by his depression, it is doubtful that they were its cause. Rather, his posthumous diagnosis of bipolarity has been accepted as the root cause of his erratic mood.[10]

I like how those math dudes can get all deep with numbers, but still need a liberal arts major to look shit up on Wikipedia for them:

Cantor suffered his first known bout of depression in 1884.[20] Criticism of his work weighed on his mind: every one of the fifty-two letters he wrote to Mittag-Leffler in 1884 attacked Kronecker. A passage from one of these letters is revealing of the damage to Cantor's self-confidence:

"???I don't know when I shall return to the continuation of my scientific work. At the moment I can do absolutely nothing with it, and limit myself to the most necessary duty of my lectures; how much happier I would be to be scientifically active, if only I had the necessary mental freshness."[21] ???

This emotional crisis led him to apply to lecture on philosophy rather than mathematics. He also began an intense study of Elizabethan literature in an attempt to prove that Francis Bacon wrote the plays attributed to Shakespeare (see Shakespearean authorship question); this ultimately resulted in two pamphlets, published in 1896 and 1897.[22]

Cantor recovered soon thereafter, and subsequently made further important contributions, including his famous diagonal argument and theorem. However, he never again attained the high level of his remarkable papers of 1874???1884. He eventually sought a reconciliation with Kronecker, which Kronecker graciously accepted. Nevertheless, the philosophical disagreements and difficulties dividing them persisted. It was once thought that Cantor's recurring bouts of depression were triggered by the opposition his work met at the hands of Kronecker.[9] While Cantor's mathematical worries and his difficulties dealing with certain people were greatly magnified by his depression, it is doubtful that they were its cause. Rather, his posthumous diagnosis of bipolarity has been accepted as the root cause of his erratic mood.[10]

easy there, player. you left out this part:

He died on January 6, 1918 in the sanatorium where he had spent the final year of his life.

Take your pick of other sources which I'm sure you can find yourself. He spent much of the last 20 years of his life in and out of sanatoria for mental illness.

The whole mental illness interacting with his mathematical ideas is of course debatable and is just part of legend/folklore.

## Comments

Sixty-Nine Dude![/b]

The Auryn is an ouroboros which is another sign for Infinity.

- spidey

hmmm... not quite the rigorous mathematical solution I was searching for.

But what the hell

Step up and receive your inaugural Roy Ayers Award for Sun Ra ish Cosmic Deepness

I think the solution was

Atreyu = 1

Bastian = -1

the Child like Empress = X

Infinity + 1 + X * 0 + -1 = Infinity

I'll take that Roy Ayers award though.

- spidey

I think it had something to do with, reality represents infinity, whereas Fantasia represents -infinity.

Google has failed me again. Any MIT finite theorists wanna help me out?

- spidey

I think I figured it out..

-infinity + -1 + X * 0 = infinity + 1 - mother

factoring in that

FANTASIA = -Infinity

REALITY = Infinity

- diego

vajdaij = reincarnation of Ramanujan

Jesus Christ, they buried Johnny in Boca? That's fucked up.

There are various ways to put some meaning to "infinity" mathematically, and depending on that meaning, you get various types of infinity.

One way is to talk about "cardinal numbers" which just takes a set, say {a,b,c}, and assign the number "3" to any set which can be put into one-to-one correspondence with this set. So the set {1,2,3} has cardinality 3 since

1 --> a

2 --> b

3 --> c

is a one-to-one correspondence of {1,2,3} with {a,b,c}.

Now, the first set one might think of as being infinite is the set of all positive integers, {1,2,3,4,5,...}. So, let's call every set that is in one-to-one correspondence with this set as "infinite" (this cardinal number is actually called "aleph-0", as in the Hebrew letter aleph). Then the set of all even positive numbers {2,4,6,8,...} is has the same infinite cardinality since

1 --> 2

2 --> 4

n --> 2n

gives a general one-to-one correspondence between {1,2,3,4,...} and {2,4,6,8,...}.

Now consider the set of all strings of 1's and 0's that are this kind of"infinite". So, 1111111...., the string of all 1's is one of these, or 101010101010... of alternating 1's and 0's is one of these. Around 1900, Cantor proved that the set of all such strings is a different kind of infinity than the set {1,2,3,...}. That is, there is no one-to-one correspondence between the set {1,2,3,...} and the set of all such strings. The proof is by "contradiction". That is, suppose these are the same type of infinity, so that we do have a correspondence. That means we can list the strings in some order, with some string being first, another being second, and so on. The idea is to find a string that cannot be in this list no matter what the list is. If the list is something like

110010100...

001001010...

110010100...

111100111...

and so on,

then consider the string 0110.., which we make by changing the first digit of the first string, the second digit of the second string, third digit of the third string, and so on. So, just go down the diagonal and switch 0's to 1's and 1's to 0's. Doing this, no matter what list we have, this always gives a string not in the list, since it will differ from every single other string by at least one digit.

Cantor went crazy when he discovered this, and spent the rest of his life in a mental hospital.

But there are other ways to look at infinities. There's a great book called "Surreal numbers" by Donald Knuth that constructs another kind of infinities. But one thing you can say about the argument that 0=1 is that the mistake is that infinity-infinity is not necessarily 0. In the infinity above, infinity-infinity can be infinity, since if you take the set {2,4,6,8,...} away from the set {1,2,3,4,...}, you are left with {1,3,5,7,...}, which is still infinite.

------------ thanks!

Honestly, I really don't have a lot of experience w/ Cantor sets and all that. It looks like bluesnaq can pick up the slack, though.

I am an authority on math. Herein lies the problem with your sons deduction. The following operations are well-defined when dealing with infinity in real analysis:

1 + infinity = infinity

1 / infinity = 0

The following operations are NOT well-defined when dealing with infinity in real analysis:

0 * infinity = not defined

infinity - infinity = not defined

What your son did was the following:

1 + infinity = infinity

therefore

1 + infinity - infinity = infinity - infinity

therefore

1 + 0 = 0

therefore

1 = 0

As you can see he was wrong in stating "infinity - infinity = 0" when in fact "infinity - infinity" is not defined at all.

The most startling conclusion when dealing with infinities is the following. We can define a "countable" set of numbers as a set that can be indexed by the natural numbers. Examples are the natural numbers, the even numbers, the odd numbers, the integers, etc. However, it can be shown that the rational numbers are countable.

And since the union of a countable set and a countable set is still a countable set, in combination with the fact that the real numbers is the union of the rational numbers and the irrational numbers and is in fact, uncountable... this means that there are MORE irrational numbers than rational numbers.

HOOO WEE!

I don't know, it seems exactly the type of thing a crazy man could construct.

I know he, at some point, spent the rest of his life in a mental institution. Not sure of the dates.

Also, subtraction can be well-defined on infinite cardinals (as long as the first is at least as big as the second). In that case, an infinite cardinal minus an equal or smaller infinite cardinal is defined to be the first larger or equal cardinal.

In the realm of surreal numbers, all kinds of operations on infinities is defined, even calculus.

Therefore

Frank Sinatra = 0

HAHAHAHA!

take it to waxidermy for another 20 pager

I love to see more blood spilled on that site

ABSOLUTELY WRONG. There is no point at which the very large begins to merge with the infinite. A trillion is no closer to the infinite than the number 7. Infinite classess need to be treated differently to finite classes and treating the infinite as just a very big number will inevitably lead you to error

Skel tell your 11 year old son that he is a dumbass who is not on dolo's level.

Infinite - infinite = infinite

infinite / infinite = infinite

infinite * infinite = infinite

infinite + infinite = infinite

You tell him

[email]cagefightinghardasfkkk11yrold@willtraveltheworldtofightanyonewhoflamesme.com[/email]

I missed this thread first time out.

In terms of math and philosophy the Greeks and Romans did not care for either infinity or zero.

There is no zero in Roman numerals.

For Western math and philosophy, we see that it wasn't until very recently, with people like Cantor, that we started to get a grip on infinity.

When I was a kid I was told the all the grains of sand are infinite.

They are not, in theory, they can be counted.

I was told that the universe is infinite.

Stephen Hawkins tells me it is finite.

easy there, player. you left out this part:

Take your pick of other sources which I'm sure you can find yourself. He spent much of the last 20 years of his life in and out of sanatoria for mental illness.

The whole mental illness interacting with his mathematical ideas is of course debatable and is just part of legend/folklore.