is this maths proof acceptable?
prove n^3 + 2 is not divisible by 8.
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
is that acceptable proof for a level maths? thanks
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
is that acceptable proof for a level maths? thanks
(edited 4 years ago)
Sounds ok to me.
Original post by Gent2324
prove 8n^3 + 2 is not divisible by 8.
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
is that acceptable proof for a level maths? thanks
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
is that acceptable proof for a level maths? thanks
Original post by mqb2766
Sounds ok to me.
wait i wrote it down wrong its actually meant to say prove n^3 + 2 is not divisibly by 8, not 8n^3 +2, would it still be fine to do that proof?
Can you edit / reply with the "correct" info?
Original post by Gent2324
wait i wrote it down wrong its actually meant to say prove n^3 + 2 is not divisibly by 8, not 8n^3 +2, would it still be fine to do that proof?
Original post by mqb2766
Can you edit / reply with the "correct" info?
prove n^3 + 2 is not divisible by 8.
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
i saw this on reddit as it came up on this years as paper, they said: Suppose 8m^3+2 were divisible by 8, so that it is equal to 8n for some integer n. Then 8m^3+2=8n so that 2=8n-8m^3=8(n-m^3). Which would mean that 2 is divisible by 8.
but i thought the question asked for 8(n^3 +2), turns out theres no 8. so is that proof still acceptable as i kind of added an 8 in from nowhere on the 3rd line
How do you get the 8* (x^3) on line 3?
That was ok in the Original version you posted but now it magically appears? I can't see this would be valid as stands.
A tiny bit in front of it could be to show n must be even, hence the Original 8n^3+2 would be an ok statement, hence the Original proof would be ok.
That was ok in the Original version you posted but now it magically appears? I can't see this would be valid as stands.
A tiny bit in front of it could be to show n must be even, hence the Original 8n^3+2 would be an ok statement, hence the Original proof would be ok.
Original post by Gent2324
prove n^3 + 2 is not divisible by 8.
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
i saw this on reddit as it came up on this years as paper, they said: Suppose 8m^3+2 were divisible by 8, so that it is equal to 8n for some integer n. Then 8m^3+2=8n so that 2=8n-8m^3=8(n-m^3). Which would mean that 2 is divisible by 8.
but i thought the question asked for 8(n^3 +2), turns out theres no 8. so is that proof still acceptable as i kind of added an 8 in from nowhere on the 3rd line
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
i saw this on reddit as it came up on this years as paper, they said: Suppose 8m^3+2 were divisible by 8, so that it is equal to 8n for some integer n. Then 8m^3+2=8n so that 2=8n-8m^3=8(n-m^3). Which would mean that 2 is divisible by 8.
but i thought the question asked for 8(n^3 +2), turns out theres no 8. so is that proof still acceptable as i kind of added an 8 in from nowhere on the 3rd line
(edited 4 years ago)
Original post by Gent2324
prove n^3 + 2 is not divisible by 8.
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
i saw this on reddit as it came up on this years as paper, they said: Suppose 8m^3+2 were divisible by 8, so that it is equal to 8n for some integer n. Then 8m^3+2=8n so that 2=8n-8m^3=8(n-m^3). Which would mean that 2 is divisible by 8.
but i thought the question asked for 8(n^3 +2), turns out theres no 8. so is that proof still acceptable as i kind of added an 8 in from nowhere on the 3rd line
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
i saw this on reddit as it came up on this years as paper, they said: Suppose 8m^3+2 were divisible by 8, so that it is equal to 8n for some integer n. Then 8m^3+2=8n so that 2=8n-8m^3=8(n-m^3). Which would mean that 2 is divisible by 8.
but i thought the question asked for 8(n^3 +2), turns out theres no 8. so is that proof still acceptable as i kind of added an 8 in from nowhere on the 3rd line
This is still a mess of a post. I'm not even sure what you're asking, but obviously misreading the question would lose you marks, but using the idea of contradiction would give a mark or two.
Original post by RDKGames
This is still a mess of a post. I'm not even sure what you're asking, but obviously misreading the question would lose you marks, but using the idea of contradiction would give a mark or two.
sorry let me ask it here, ignore all the other posts i made:
prove n^3 + 2 is not divisible by 8.
If n is odd, then n^3+2 is odd, so isn't divisible by 8.
If n is even, then n = 2x where x is an integer. Then n^3 +2 = 8x^3 +2
proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
is that correct proof?
(edited 4 years ago)
Sounds ok now.
Original post by Gent2324
sorry let me ask it here, ignore all the other posts i made:
prove n^3 + 2 is not divisible by 8.
If n is odd, then n^3+2 is odd, so isn't divisible by 8.
If n is even, then n = 2x where x is an integer. Then n^3 +2 = 8x^3 +2
proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
is that correct proof?
prove n^3 + 2 is not divisible by 8.
If n is odd, then n^3+2 is odd, so isn't divisible by 8.
If n is even, then n = 2x where x is an integer. Then n^3 +2 = 8x^3 +2
proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
is that correct proof?
Original post by Gent2324
sorry let me ask it here, ignore all the other posts i made:
prove n^3 + 2 is not divisible by 8.
proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
is that correct proof?
prove n^3 + 2 is not divisible by 8.
proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.
is that correct proof?
Pretty much, though I feel uneasy with you saying "for 2 to be divisible by 8(n-x^3)" when the natural thing to say after "2 is divisible by 8" is "it's impossible for 2 to be divisible by 8" hence the contradiction.
Also, it's slightly awkward when you take their and use in its place. You should just say "Suppose is div. by 8, then for some integer "
Original post by mqb2766
Sounds ok now.
ok thank you for help, i found out that the reddit post i was referring to was actually a reply of someone who got to n^3 +2 = 8x^3 +2 hence why it wasnt proof on its own
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