- #1

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i think it can be done by least upper bounds, but i dun know wat is the exact prove.

- Thread starter andilus
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- #1

- 8

- 0

i think it can be done by least upper bounds, but i dun know wat is the exact prove.

- #2

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Look up "Intermediate Value Theorem" or "Bolzano's Theorem."

- #3

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As another poster suggested, the intermediate value theorem guarantees there is an x in [a,b] where f(x) = 0. And your idea of using the lub is a good one. So let

[itex] z = [/itex] lub [itex]\{ x \in [a,b] | f(x) = 0\} [/itex]

So what you need to show to finish the problem is:

1. z is in [a,b]

2. f(z) = 0

3. No value x > z in [a,b] satisfies f(x) = 0.

[itex] z = [/itex] lub [itex]\{ x \in [a,b] | f(x) = 0\} [/itex]

So what you need to show to finish the problem is:

1. z is in [a,b]

2. f(z) = 0

3. No value x > z in [a,b] satisfies f(x) = 0.

Last edited:

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