dnejfn
Badges: 12
Rep:
?
#1
Report Thread starter 4 months ago
#1
not sure how to do this.Name:  Screenshot 2021-01-22 at 12.32.07.png
Views: 78
Size:  25.5 KB
0
reply
mqb2766
Badges: 19
Rep:
?
#2
Report 4 months ago
#2
(Original post by dnejfn)
not sure how to do this.Name:  Screenshot 2021-01-22 at 12.32.07.png
Views: 78
Size:  25.5 KB
Assume there is a greatest multiple, then show the contradiction.
It really would help to be specific about your problem.
0
reply
dnejfn
Badges: 12
Rep:
?
#3
Report Thread starter 4 months ago
#3
(Original post by mqb2766)
Assume there is a greatest multiple, then show the contradiction.
It really would help to be specific about your problem.
i dont understand what they mean by greatest multiple
0
reply
DFranklin
Badges: 18
Rep:
?
#4
Report 4 months ago
#4
(Original post by dnejfn)
i dont understand what they mean by greatest multiple
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.
0
reply
dnejfn
Badges: 12
Rep:
?
#5
Report Thread starter 4 months ago
#5
(Original post by 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.
if N is a multiple of 5 then let N= 5a
0
reply
mqb2766
Badges: 19
Rep:
?
#6
Report 4 months ago
#6
(Original post by dnejfn)
if N is a multiple of 5 then let N= 5a
And the contradiction part ..
0
reply
dnejfn
Badges: 12
Rep:
?
#7
Report Thread starter 4 months ago
#7
(Original post by mqb2766)
And the contradiction part ..
5a+1?
0
reply
DFranklin
Badges: 18
Rep:
?
#8
Report 4 months ago
#8
(Original post by dnejfn)
5a+1?
How is that a contradiction?
0
reply
dnejfn
Badges: 12
Rep:
?
#9
Report Thread starter 4 months ago
#9
(Original post by DFranklin)
How is that a contradiction?
idk im so confused about this question
0
reply
Aloe Striata
Badges: 19
Rep:
?
#10
Report 4 months ago
#10
(Original post by dnejfn)
idk im so confused about this question
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?
Last edited by Aloe Striata; 4 months ago
0
reply
Aloe Striata
Badges: 19
Rep:
?
#11
Report 4 months ago
#11
idk why the '+' doesn't show in my post.
I mean N + 1 and N + 1 > N
0
reply
dnejfn
Badges: 12
Rep:
?
#12
Report Thread starter 4 months ago
#12
(Original post by 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?
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.
0
reply
Aloe Striata
Badges: 19
Rep:
?
#13
Report 4 months ago
#13
(Original post by 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.
but how would 5a + 1 be a multiple of 5? is 1 divisible by 5?
0
reply
mqb2766
Badges: 19
Rep:
?
#14
Report 4 months ago
#14
(Original post by 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.
But it's not a multiple of 5. You have to play by the rules of the game.
0
reply
dnejfn
Badges: 12
Rep:
?
#15
Report Thread starter 4 months ago
#15
(Original post by mqb2766)
But it's not a multiple of 5. You have to play by the rules of the game.
so its 5a+5>N instead
0
reply
Aloe Striata
Badges: 19
Rep:
?
#16
Report 4 months ago
#16
(Original post by dnejfn)
so its 5a+5>N instead
Yes
0
reply
Aloe Striata
Badges: 19
Rep:
?
#17
Report 4 months ago
#17
(Original post by dnejfn)
so its 5a 5>N instead
Also, for future reference, keep it simple. Say something like:
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
0
reply
dnejfn
Badges: 12
Rep:
?
#18
Report Thread starter 4 months ago
#18
(Original post by ilovephysmath)
Yes
so then that's the answer.
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.
0
reply
mqb2766
Badges: 19
Rep:
?
#19
Report 4 months ago
#19
(Original post by dnejfn)
so its 5a+5>N instead
It would be better to write
5(a+1) > 5a = N
0
reply
Final Fantasy
Badges: 20
Rep:
?
#20
Report 4 months ago
#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.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Do you think receiving Teacher Assessed Grades will impact your future?

I'm worried it will negatively impact me getting into university/college (74)
38.14%
I'm worried that I’m not academically prepared for the next stage in my educational journey (19)
9.79%
I'm worried it will impact my future career (12)
6.19%
I'm worried that my grades will be seen as ‘lesser’ because I didn’t take exams (48)
24.74%
I don’t think that receiving these grades will impact my future (25)
12.89%
I think that receiving these grades will affect me in another way (let us know in the discussion!) (16)
8.25%

Watched Threads

View All
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise