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Current time: 26th September 2017, 10:45
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Are you into mathematics? Do you have any cake?

Your good friend (with benefits) and trusted confidant,
W.W. Whateverist, esq.
"There remain four irreducible objections to religious faith: that it wholly misrepresents the origins of man and the cosmos, that because of this original error it manages to combine the maximum servility with the maximum of solipsism, that it is both the result and the cause of dangerous sexual repression, and that it is ultimately grounded on wishthinking." ~Christopher Hitchens, god is not Great
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9th February 2017, 13:35
(This post was last modified: 9th February 2017, 13:48 by pool the matey. Edited 4 times in total.)
What's so "trololololol" about my question?
According to you guys it's absolutely impossible to divide a cake with no one but perfectly possible to add absolutely nothing to a cake. You can't just "add" nothing to a cake, that would defeat the purpose of the addition operation in the first place, no addition took place there. So why is it okay to add nothing to a cake but not okay to divide a cake among no one? Seems like a perfectly reasonable question to me. RE: Are you into mathematics? Do you have any cake?
9th February 2017, 14:23
(This post was last modified: 9th February 2017, 14:43 by Whateverist. Edited 3 times in total.)
(9th February 2017, 13:35)pool the great Wrote: What's so "trololololol" about my question? As Alex put it, division asks a more involved question than addition; it isn't just "what do you get?" Division really asks: if you give an equal portion of an x amount to each of y, how much does each y get? Implicit in the question is the idea that you hand out all of the starting amount, x. If upon completing the division there is anything remaining, you simply didn't do it right and we can't call that division. When you divide by 1 you aren't left with the entire cake, it was handed out to just one person. If it was retained it was never divided up. A good way to think of division is as the inverse of multiplication. Where multiplication asks for repeated addition (eg, what is the sum of 4 threes), division asks if the sum of 4 of something is 12, what is that something or what would you need 4 of to total 12? So for the cake problem where you have 4 to serve you might ask: how much of the cake should each receive in order to use it up while giving each an equal share? Answer: Each should receive a fourth of the cake. But to divide it equally among 0 people, there isn't any amount which would use up the entire cake. Since there is no way to accomplish the giving out an equal amount to zero people in such a way as to hand out all of the cake, the problem has no solution and really the question makes no sense. The operation is being employed in a way that betrays a misunderstanding of its purpose and proper application.
Your good friend (with benefits) and trusted confidant,
W.W. Whateverist, esq. RE: Are you into mathematics? Do you have any cake?
9th February 2017, 14:45
(This post was last modified: 9th February 2017, 15:36 by Kernel Sohcahtoa. Edited 3 times in total.)
(9th February 2017, 13:35)pool the great Wrote: What's so "trololololol" about my question? pool the great Wrote:If I divide my cake with nobody how much cake will each person have? Zero. So 1/0=0? Hello, sir. I have noticed that in your posts 1/0 was equated to 1. In order to understand why this is not correct, it may be useful to understand how the graph of 1/x looks and behaves Now, notice that once we get to the values in between 0 and 1, the values of Y start shooting up. For example, 1 divided by x=1/2 yields y=2, 1 divided by x=1/4 yields y=4, 1 divided by x=1/1,000 yields y=1,000, 1 divided by x=1/1,000,000,000 yields y=1,000,000,000 and so on. Hence, the closer x gets to zero (zero being the limit of this function in this case), then this will cause the y value to get closer to infinity. Hence, 1/0 would result in infinity, which is not defined. * Also notice that we can observe the same thing in between the values of 1 and 0: as x approaches zero from the left side, then y will approach negative infinity Now, the operation of 1+0 is valid, because zero is the identity element of addition: this means that if we add 0 to any real number, then we will get that same real number. For example, 1+0=1;100+0=100; and so on. This may be better illustrated by seeing a graph of 1+x *in terms of division and multiplication, the identity element is 1 (100/1=100, 2/1=2, 1/1=1 and so on). Hence, when you are not sharing the cake with your friends, then that implies that you get the whole cake, which is equivalent to dividing by the identity element of 1, or 1/1=1. Here's a graph of y=1+x, which we can equivalently call y=x+1: Notice that for any x value in the domain (all of the possible values that can be inputted into x of our function x+1) of real numbers, y will have a value in the range (all of the outputs that our produced from inputting x into our function) of real numbers (in fact, each x will be mapped to exactly one y value). Hence, each x value will produce a y value that is defined. For example, 1+ x=0 yields y=1. Hence, adding by zero is valid, because zero is the identity element of addition: it will produce that same value that we are adding zero to. However, dividing by zero is invalid, because that would result in infinity and infinity is not defined. I hope this has been useful in answering your inquiry, sir. Live long and prosper. Edit P.S. Regarding y=1/x and the cake problem, we would need to restrict our domain to the natural numbers or positive integers {1,2,3,4,5,6,7,.......} in order for your cake cutting division problem to make sense.
"I'm fearful when I see people substituting fear for reason." Klaatu, from The Day The Earth Stood Still (1951)

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