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#1 2010-01-07 11:27:28

elite-mathlete
Member
Registered: 2006-07-16
Posts: 40

"Such that"

Good thing I dug up my old account, I got College Algebra class.

Could anyone explain to me the concept of "Such that" which is this symbol: |

I understand where and how it's used, but the reasoning behind why it's called that has flown over my head.


Maybe the helicopter, maybe it's made of chocolate.

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#2 2010-01-07 11:45:31

elite-mathlete
Member
Registered: 2006-07-16
Posts: 40

Re: "Such that"

For instance:

(2,9) {x|2<x<9}


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#3 2010-01-07 12:03:08

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: "Such that"

{x | 2 < x < 9}

When you read this out loud, it goes:

x is such that 2 is less than x and x is less than 9.

That's why we call '|' that symbol "such that".


"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..."

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#4 2010-01-07 13:06:10

elite-mathlete
Member
Registered: 2006-07-16
Posts: 40

Re: "Such that"

So it's like "is" or "equals"?


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#5 2010-01-07 13:16:39

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: "Such that"

No, it's all numbers such that they satisfy the property 2 < x < 9.  The left of the '|' is the place where your drawling your elements from (in this case, it's all numbers).  The right of the '|' is the property that those elements must satisfy.  For example:

This is all numbers x in the set [0, infinity) such that 1/x is greater than 1.


"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..."

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#6 2010-01-07 14:21:48

elite-mathlete
Member
Registered: 2006-07-16
Posts: 40

Re: "Such that"

Ah I see, so it means "X could be anything that falls under these conditions", like a reversed if statement.

Last edited by elite-mathlete (2010-01-07 14:22:47)


Maybe the helicopter, maybe it's made of chocolate.

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