# proof by contradiction

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#2

(Original post by

not sure how to do this.

**dnejfn**)not sure how to do this.

It really would help to be specific about your problem.

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(Original post by

Assume there is a greatest multiple, then show the contradiction.

It really would help to be specific about your problem.

**mqb2766**)Assume there is a greatest multiple, then show the contradiction.

It really would help to be specific about your problem.

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#4

(Original post by

i dont understand what they mean by greatest multiple

**dnejfn**)i dont understand what they mean by greatest multiple

(a) N is a multiple of 5

(b) if M is a multiple of 5 it is always true that M<=N.

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(Original post by

N is a greatest multiple of 5 if

(a) N is a multiple of 5

(b) if M is a multiple of 5 it is always true that M<=N.

**DFranklin**)N is a greatest multiple of 5 if

(a) N is a multiple of 5

(b) if M is a multiple of 5 it is always true that M<=N.

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#6

(Original post by

if N is a multiple of 5 then let N= 5a

**dnejfn**)if N is a multiple of 5 then let N= 5a

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(Original post by

How is that a contradiction?

**DFranklin**)How is that a contradiction?

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#10

(Original post by

idk im so confused about this question

**dnejfn**)idk im so confused about this question

Prove by contradiction that there is no largest integer.

let us assume that there is a largest integer, N.

but when we add 1 to N we get N 1 and N 1>N. This contradicts our statement, so there is no largest integer.

These kinds of questions follow the same pattern, even if the context changes a little. Now how do you think we'll tackle your question?

Last edited by Aloe Striata; 4 months ago

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(Original post by

Look, numbers are infinite right? I'll give you an example that might help:

Prove by contradiction that there is no largest integer.

let us assume that there is a largest integer, N.

but when we add 1 to N we get N 1 and N 1>N. This contradicts our statement, so there is no largest integer.

These kinds of questions follow the same pattern, even if the context changes a little. Now how do you think we'll tackle your question?

**ilovephysmath**)Look, numbers are infinite right? I'll give you an example that might help:

Prove by contradiction that there is no largest integer.

let us assume that there is a largest integer, N.

but when we add 1 to N we get N 1 and N 1>N. This contradicts our statement, so there is no largest integer.

These kinds of questions follow the same pattern, even if the context changes a little. Now how do you think we'll tackle your question?

but then when you add 1, 5a+1>N which contradicts the statement.

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#13

(Original post by

so if we assume N is a multiple of 5, N = lets say 5a

but then when you add 1, 5a+1>N which contradicts the statement.

**dnejfn**)so if we assume N is a multiple of 5, N = lets say 5a

but then when you add 1, 5a+1>N which contradicts the statement.

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#14

**dnejfn**)

so if we assume N is a multiple of 5, N = lets say 5a

but then when you add 1, 5a+1>N which contradicts the statement.

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(Original post by

But it's not a multiple of 5. You have to play by the rules of the game.

**mqb2766**)But it's not a multiple of 5. You have to play by the rules of the game.

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#17

(Original post by

so its 5a 5>N instead

**dnejfn**)so its 5a 5>N instead

N is the greatest multiple of 5. But since N 5 > N, and N 5 is also a multiple of 5, there is no greatest multiple of 5. Keep the variables to a minimum if you can help it. Avoiding clutter makes things clearer.

Last edited by Aloe Striata; 4 months ago

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(Original post by

Yes

**ilovephysmath**)Yes

so if we assume N is a multiple of 5, let N= 5a

but then when you add 1, 5a+5>N which contradicts the statement. So there is no greatest multiple of 5.

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#19

(Original post by

so its 5a+5>N instead

**dnejfn**)so its 5a+5>N instead

5(a+1) > 5a = N

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#20

- prove by contradiction that there is no greatest multiple of 5

N = greatest multiple of 5

10 = multiple of 5 (2 * 5 = 10)

N > 10

10 * N cannot be greatest multiple of 5 than N because N is the greatest multiple 5. N > 10N but 10 * N is greater than N... so we have a contradiction.

N = greatest multiple of 5

10 = multiple of 5 (2 * 5 = 10)

N > 10

10 * N cannot be greatest multiple of 5 than N because N is the greatest multiple 5. N > 10N but 10 * N is greater than N... so we have a contradiction.

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