Editing 1381: Margin
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What it seems he did not realize, is that it would be impossible to read the proof if the writer actually was able to compress his proof to fit in the margin. This is because you would need to know the algorithm described in the proof before you could decompress the proof text so you can read it. So he could actually have used this trick instead, writing that he had compressed it into - say a dot "'''.'''" - and then people would have to find his proof to read it. And since they cannot find such a proof - they could not check his dot. Unfortunately this would also have backfired - because there is already a {{w|Pigeonhole principle#Uses and applications|proof that this is not possible}}! | What it seems he did not realize, is that it would be impossible to read the proof if the writer actually was able to compress his proof to fit in the margin. This is because you would need to know the algorithm described in the proof before you could decompress the proof text so you can read it. So he could actually have used this trick instead, writing that he had compressed it into - say a dot "'''.'''" - and then people would have to find his proof to read it. And since they cannot find such a proof - they could not check his dot. Unfortunately this would also have backfired - because there is already a {{w|Pigeonhole principle#Uses and applications|proof that this is not possible}}! | ||
| − | Another thing that he probably didn't realize, is that finding a proof for something being possible does not necessarily mean inventing an actual algorithm to do that particular thing. If the person claimed having found a {{w| | + | Another thing that he probably didn't realize, is that finding a proof for something being possible does not necessarily mean inventing an actual algorithm to do that particular thing. If the person claimed having found a {{w|Constructive proof|non-constructive proof}} for such an algorithm, his statement at least wouldn't contradict itself. |
The title text, yet another [[:Category:Protip|protip]], makes a reference to the {{w|Shannon–Hartley theorem}}, which limits the maximum rate at which information can be transmitted. Setting the font size of text only changes its ''representation'' on the screen, and not the actual characters themselves. Trying to decrease the amount of space needed to store or transmit it like advised would be nonsensical. Another possible interpretation is that if you set the font size to 0, the text cannot be seen, and therefore, nothing is being transmitted period. | The title text, yet another [[:Category:Protip|protip]], makes a reference to the {{w|Shannon–Hartley theorem}}, which limits the maximum rate at which information can be transmitted. Setting the font size of text only changes its ''representation'' on the screen, and not the actual characters themselves. Trying to decrease the amount of space needed to store or transmit it like advised would be nonsensical. Another possible interpretation is that if you set the font size to 0, the text cannot be seen, and therefore, nothing is being transmitted period. | ||
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*Fermat's Last Theorem states that no three positive integers ''a'', ''b'', and ''c'' can satisfy the equation ''a''<sup>''n''</sup> + ''b''<sup>''n''</sup> = ''c''<sup>''n''</sup> for any integer value of ''n'' greater than two. | *Fermat's Last Theorem states that no three positive integers ''a'', ''b'', and ''c'' can satisfy the equation ''a''<sup>''n''</sup> + ''b''<sup>''n''</sup> = ''c''<sup>''n''</sup> for any integer value of ''n'' greater than two. | ||
| − | **In the case with n=2, a b and c are the sides of a {{w|Pythagorean theorem|right triangle}}. There are an infinite number of integer solutions for a, b and c, such as ''3''<sup>''2''</sup> + ''4''<sup>''2''</sup> = ''5''<sup>''2''</sup>. This was known to Euclid | + | **In the case with n=2, a b and c are the sides of a {{w|Pythagorean theorem|right triangle}}. There are an infinite number of integer solutions for a, b and c, such as ''3''<sup>''2''</sup> + ''4''<sup>''2''</sup> = ''5''<sup>''2''</sup>. This was known to Euclid. |
*Fermat's Last Theorem was {{w|Wiles' proof of Fermat's Last Theorem|solved}} in 1995 by {{w|Andrew Wiles}} with some assistance by {{w|Richard Taylor (mathematician)|Richard Taylor}} who helped him close a gap in his original proof from 1993. | *Fermat's Last Theorem was {{w|Wiles' proof of Fermat's Last Theorem|solved}} in 1995 by {{w|Andrew Wiles}} with some assistance by {{w|Richard Taylor (mathematician)|Richard Taylor}} who helped him close a gap in his original proof from 1993. | ||
**The proof involved some of the most complicated mathematics used today, and it has been speculated that only a handful of people in the world would be able to understand it. | **The proof involved some of the most complicated mathematics used today, and it has been speculated that only a handful of people in the world would be able to understand it. | ||
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[[Category:Protip]] | [[Category:Protip]] | ||
[[Category:Math]] | [[Category:Math]] | ||
| − | + | --DrMath 06:10, 18 October 2016 (UTC) | |
