# What is Infinity?

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16 years ago
#21
(Original post by 2776)
But the sigs are the truth. The world must know the thoughts and speeches of the other members of the forum.
I agree.
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16 years ago
#22
(Original post by 2776)
But the sigs are the truth. The world must know the thoughts and speeches of the other members of the forum.
i sense hyprocisy, did you not state young members use this forum not long ago? The example you're setting, i mean really!
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16 years ago
#23
The concept of infinity has tantalized and sometimes troubled mankind even longer. Zeno of Elea (495 BC?-425 BC?), an early Greek thinker, is remembered for his paradoxes of motion that are rooted in deep questions about the nature of time and space and in some misconceptions about infinity. Most religions attempt to explain in their own ways the mysteries and vagaries of the infinite.

In the early 1600's Galileo began to show signs of a modern attitude toward the infinite, when he proposed that "infinity should obey a different arithmetic than finite numbers." But it was not until the late 19th century that Georg Cantor (1845-1918), a German mathematician, finally put infinity on a firm logical foundation and described a way to do arithmetic with infinite quantities useful to mathematics. His basic definition was simple: a collection is infinite, if some of its parts are as big as the whole. For example, even though from one point of view the entire list of numbers we count with {1,2,3,4,5,.......} is twice as large as the list of even numbers {2,4,6,8,10,.......}, the two lists can be matched-up in a one-to-one fashion.

So the two lists are exactly the same size, infinite. (This idea has been amusingly elaborated in the story of "The Hotel Ad Infinitum" as told by David Stacy.)
Cantor was able to demonstrate that there are different sizes of infinity. The infinity of decimal numbers that are bigger than zero but smaller than one is greater than the infinity of counting numbers. (Click to see Cantor's "diagonalization proof.")

Here's a question that might tax your intuition: There are infinitely many COUNTING NUMBERS and infinitely many FRACTIONS. Which infinity is greater? Think about it, then click for an explanation.

The bottom line is that weird things can happen with infinity.

One more illustration: There are the same number of points on a short semicircular arc as there are on an entire unbounded line.

The arrows show how to match-up every point on the line with a unique point on the semicircle.
Can YOU demonstrate that the infinities of points on a big circle and a little circle are exactly the same size?
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16 years ago
#24
What happened to supporting me?

Change it back, and you are once again worthy of a place in my sig.
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16 years ago
#25
(Original post by Tinykates)
no need 4 that tone
why did you choose blue?
Blue's my favourite colour.
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16 years ago
#26
What is it we're supposed to vote for anyway (and don't say 2776)?
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16 years ago
#27
(Original post by bono)

Change it back, and you are once again worthy of a place in my sig.
and now...
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#28
blue is my favorite hence my balls are blue
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16 years ago
#29
and now...

*goes off to change sig*
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16 years ago
#30
(Original post by bono)

*goes off to change sig*
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16 years ago
#31
(Original post by 2776)
Indeed one of the great mystery of life.
you have posted it on a thread once
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16 years ago
#32
(Original post by Blackballs)
The concept of infinity has tantalized and sometimes troubled mankind even longer. Zeno of Elea (495 BC?-425 BC?), an early Greek thinker, is remembered for his paradoxes of motion that are rooted in deep questions about the nature of time and space and in some misconceptions about infinity. Most religions attempt to explain in their own ways the mysteries and vagaries of the infinite.

The arrows show how to match-up every point on the line with a unique point on the semicircle.
Can YOU demonstrate that the infinities of points on a big circle and a little circle are exactly the same size?
Good copy/paste job.
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16 years ago
#33
(Original post by bono)
Blue's my favourite colour.
fair enough. maybe i was reading into it too much
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16 years ago
#34
(Original post by _EMMA_)
you have posted it on a thread once
Indeed, the truth is buried in the detrius of threads making up the rest of the forum.
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16 years ago
#35
(Original post by 2776)
Good copy/paste job.
Damn, I thought it was original.

THE CADSTER IS BACK!!!!!! WITH A VENGENACE!
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16 years ago
#36
(Original post by bono)

*goes off to change sex*
What the hell
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16 years ago
#37
(Original post by 2776)
Indeed, the truth is buried in the detrius of threads making up the rest of the forum.
2776, What colour do you want the writing to be?

is blue ok, or you prefer another colour?
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16 years ago
#38
(Original post by 2776)
But the sigs are the truth. The world must know the thoughts and speeches of the other members of the forum.
ahhh the days of russell the love muscle are back again.....

*we wish*
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16 years ago
#39
(Original post by bono)
Damn, I thought it was original.

THE CADSTER IS BACK!!!!!! WITH A VENGENACE!
Indeed. I am back. It time to piss this **** up!
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16 years ago
#40
(Original post by ZJuwelH)
What the hell, my **** is that tiny
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