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Mathematics (pg. 2)
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| LAdazeNYnights |
Actually
40 + 40 * 0 + 1 = ?
40 + 40 * 0 = ? - 1
40 * 0 = ? - 41
40 =(?-41) / 0
40 =undefined |
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| Vector A |
Circulate this on Facebook:
The prime factorization of any integer is unique.
Proof: Suppose that there exists at least one integer with more than one prime factorization. Then there must be a least (smallest) such integer, k. We can write k as a product of prime factors like this:
[1] k = p_0 * p_1 * p_2 * ... * p_n = q_0 * q_1 * q_2 * ... * q_n
The two lists (p_0...p_n and q_0...q_n) cannot have any primes in common -- otherwise we could factor out the non-unique prime(s) from both sides of the equation and have a smaller number with two prime factorizations, which would contradict our initial premise. It follows then that either p_0 < q_0 or q_0 < p_0. Say p_0 is the smaller of the two, and consider the following number, k':
[2] k' = k - (p_0 * q_1 * q_2 * ... * q_n)
[3] k' = (p_0 * p_1 * p_2 * ... * p_n) - (p_0 * q_1 * q_2 * ... * q_n) = p_0 * ( (p_1 * p_2 * ... * p_n) - (q_1 * q_2 * ... * q_n))
[4] k' = (q_0 * q_1 * q_2 * ... * q_n) - (p_0 * q_1 * q_2 * ... * q_n) = (q_0 - p_0) * (q_1 * q_2 * ... * q_n)
Clearly k' is smaller than k. k' is also positive, since the product (p_0 * q_1 * q_2 * ... * q_n) is smaller than k. [3] Tells us that p_0 must be a factor of k', and from [4] it follows that p_0 must be a factor of either (q_0 - p_0) or (q_1 * q_2 * ... * q_n). But p_0 cannot be a factor of the latter term, as that term produces a number smaller than k and any number smaller than k must be uniquely factorizable. So p_0 must be a factor of (q_0 - p_0), which means we can write:
q_0 - p_0 = p_0 * h
...with h being some integer. And...
q_0 = p_0 + p_0 * h = p_0 * (h + 1)
But if q_0 is a multiple of p_0, then q_0 is not prime, which means that (q_0 * q_1 * q_2 * ... * q_n) cannot be a prime factorization. So our first premise -- that at least one integer has more than one prime factorization -- must be mistaken. |
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| EddieZilker |
| ATTENTION: THE HACKERS ARE PUTTING SEXUAL VIDEOS TO YOUR NAME IN THE WALLS / PROFILES OF YOUR FRIENDS WITHOUT YOU KNOWING IT. YOU DONT SEE IT, BUT OTHER PEOPLE CAN SEE IT, AS IF THESE WERE A PUBLICATION THAT YOU MADE! ALSO, THEY'RE SENDING ...INBOX MSGS TO YOUR FRIENDS ASKING YOU TO CLICK A LINK. DON'T DO IT!! SO IF YOU RECEIVE SOMETHING FROM ME ABOUT A VIDEO OR A STRANGE INBOX MESSAGE, IT'S NOT ME! copy this in your wall. It is for the security of YOUR OWN IMAGE!!! And REPORT IT!!!!! ALSO IF U ARE ASKED TO VOTE ON A PICTURE. DO NOT GO & VOTE: IT'S A HACKER!! POST THIS TO YOUR WALL FOR YOUR FRIENDS |
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| Vector A |
| quote: | Originally posted by EddieZilker
ATTENTION: THE HACKERS ARE PUTTING SEXUAL VIDEOS TO YOUR NAME IN THE WALLS / PROFILES OF YOUR FRIENDS WITHOUT YOU KNOWING IT. YOU DONT SEE IT, BUT OTHER PEOPLE CAN SEE IT, AS IF THESE WERE A PUBLICATION THAT YOU MADE! ALSO, THEY'RE SENDING ...INBOX MSGS TO YOUR FRIENDS ASKING YOU TO CLICK A LINK. DON'T DO IT!! SO IF YOU RECEIVE SOMETHING FROM ME ABOUT A VIDEO OR A STRANGE INBOX MESSAGE, IT'S NOT ME! copy this in your wall. It is for the security of YOUR OWN IMAGE!!! And REPORT IT!!!!! ALSO IF U ARE ASKED TO VOTE ON A PICTURE. DO NOT GO & VOTE: IT'S A HACKER!! POST THIS TO YOUR WALL FOR YOUR FRIENDS |
lol. I read just now that Facebook is being flooded with some kind of porn hack.
Unfortunate time to be an FB user, I suppose. |
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| Joss Weatherby |
Wait, OP is a joke right?
Right?
RIIIIGHT?!?!?!??!?! :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: |
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| EddieZilker |
| quote: | Originally posted by Vector A
lol. I read just now that Facebook is being flooded with some kind of porn hack.
Unfortunate time to be an FB user, I suppose. |
Yup, lol.
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| Vector A |
| quote: | Originally posted by Joss Weatherby
Wait, OP is a joke right?
Right?
RIIIIGHT?!?!?!??!?! :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: :wtf: |
I would rather they just recycled the ".99999... = 1" thing or the "proof that 0 = 1" deal. Those at least have some pedagogical value.
:wtf: |
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| srussell0018 |
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| Vector A |
| ^ And that is why you are not allowed to divide by 0. |
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| LAdazeNYnights |
| quote: | Originally posted by Vector A
lol. I read just now that Facebook is being flooded with some kind of porn hack.
Unfortunate time to be an FB user, I suppose. |
This only happens to idiots who click on links like
"O M G did you see what this person said about MILEY CYRUS?? Click here now!"
Anybody stupid enough to spread that should be banned from facebook, potentially banned from the internet, and most certainly neutered. |
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