Math Is Fun Forum

Patrick

Real Member

Registered: 2006-02-24

Posts: 1,005

Re: Infinity

thinkdesigns - isn't that why it's so interresting?

Jimmymcjummingtin - You have to imagine a set

where the three dots represent an infinite amount of the preceding number. This gives you an infinite amount of 1's, followed by an infinite amount of 2's and then an infinite amount of 3's and so on. Ricky's claim is then that the set would only include 1's, since the proceding numbers wouldnt be included(you can't reach an infinite amount of 1's, which you would need to move on to filling in 2's). Dunno if it helps(or if it's correct? )

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Infinity

100% correct Patrick.  Think of it this way.  At what position in the set would there be a 2?

to me it seems mroe symbolic than mathematical, and ironically, if something is infinite, then it is beyond our understanding anyway, and so there is no point ever trying to consider what it is like because we will always fall short

When you get up to higher maths, you find that all of math is symbolic.

Infinity is not beyond our understanding.  It is beyond many peoples understanding, that is true.  But not a mathematicians.  For example:

f(x) = 1/x

We know what would happen if we reach infinity.  f(x) = 0.  Of course, we never do reach infinity, but we know what would happen if we did.

Mathematicians have been studying infinity for hundreds of years.  And we know a heck of a lot about it.  We know it has properties, just like anything else in math.  We know that if we come across it in equations, we can use tricks to get rid of it.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Infinity

Ricky denies R set

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X'(y-Xβ)=0

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Infinity

The only thing I deny is my denial.

But serious, what are you talking about George?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Infinity

Yes, but you can have a set like this:
B = { ...2,2,2,1,1,1...}

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igloo myrtilles fourmis

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Infinity

Sure you can, John.  But that set you posted is the same thing as the set {2, 2, 2.....}

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Infinity

Yeah, sure.
and you also know that

Humans have been in battle with flies, bugs and virus for hundreds of years. But that do not prove humans had solved them already.

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X'(y-Xβ)=0

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Infinity

The only thing I deny is my denial.

But serious, what are you talking about George?

the point and assumption you use is that since before 2,2,2.... there are infinite numbers (or elements) of 1,  2 can not exist in the set.

By same argument, I would say 2 in R set cannot have the chance to appear, for there are perhaps even more numbers ahead of it, and most of all you cannot find the number exactly ahead of 2.

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X'(y-Xβ)=0

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Infinity

George, you miss the major difference that R is an uncountable set while {1,1,1....2,2,2...} is countable.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Infinity

Okay, I agree since countable sets are such defined.

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X'(y-Xβ)=0

Zmurf

Member

Registered: 2005-07-31

Posts: 49

Re: Infinity

An English lesson, that's infinity isn't it?

∞ = 1/0

Try to split 1 evenly between zero groups. That would be infinity. Atleast based on the elemntary school idea that divsion is giving an equal share of x to y amount of groups.

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"When subtracted from 180, the sum of the square-root of the two equal angles of an isocoles triangle squared will give the square-root of the remaining angle squared."

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Infinity

An English lesson, that's infinity isn't it?

∞ = 1/0

Except 1/0 simply can't be done (any number times 0 gives 0, never 1), so 1/0 is "undefined".

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman