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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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For instance:
(2,9) {x|2<x<9}
Maybe the helicopter, maybe it's made of chocolate.
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{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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So it's like "is" or "equals"?
Maybe the helicopter, maybe it's made of chocolate.
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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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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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