Editing 1856: Existence Proof
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==Explanation== | ==Explanation== | ||
| + | {{incomplete|Needs more work, especially an explanation of the G() function.}} | ||
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In mathematics, an existence proof is a proof that only shows that an object with a specific property exists, but does not tell what this object is. For instance, if f is a continuous function such that f(0) = 0 and f(100) = 2, it is easy to prove that there exists an x between 0 and 100 such that f(x) = 1 (as in the comic). However, this proof gives no way to find such an x. | In mathematics, an existence proof is a proof that only shows that an object with a specific property exists, but does not tell what this object is. For instance, if f is a continuous function such that f(0) = 0 and f(100) = 2, it is easy to prove that there exists an x between 0 and 100 such that f(x) = 1 (as in the comic). However, this proof gives no way to find such an x. | ||
In many situations, a proof of existence is enough to satisfy a mathematician, but in others, it is desirable to actually identify the object whose existence has been proven. | In many situations, a proof of existence is enough to satisfy a mathematician, but in others, it is desirable to actually identify the object whose existence has been proven. | ||
| β | The full statement itself seems like a solution to some kind of {{w|function composition}} problem. Seems like what the class has proven is that if you apply certain function G(x) to a starting point of function f(0), then what it will do is just give you a value of f(x) at some other value of x, existence of which is stated to be proven | + | The full statement itself seems like a solution to some kind of {{w|function composition}} problem. Seems like what the class has proven is that if you apply certain function G(x) to a starting point of function f(0), then what it will do is just give you a value of f(x) at some other value of x, existence of which is stated to be proven. |
In the comic, [[Miss Lenhart]] (and students) take this one step further, by taking up arms to destroy the function value, which they have proven to exist. In the last panel, some students off screen begin to wonder if they are in the right class, as normal math classes do not take up swords to fight abstract concepts.{{Citation needed}} Another student remarks that they are finally in the right math class, implying that this is the kind of thing they wanted from their math curriculum all along. | In the comic, [[Miss Lenhart]] (and students) take this one step further, by taking up arms to destroy the function value, which they have proven to exist. In the last panel, some students off screen begin to wonder if they are in the right class, as normal math classes do not take up swords to fight abstract concepts.{{Citation needed}} Another student remarks that they are finally in the right math class, implying that this is the kind of thing they wanted from their math curriculum all along. | ||
