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

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

For instance:

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

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

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

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

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

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

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

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

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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