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Mathematics 16 Online
121314gifted:

Y + 13 + 5 = 36

CoolRekterizer:

What do you think?

AngeI:

What are you trying to so with this equation? cx

AngeI:

To do*

Gdeinward:

Its quite simple

mhchen:

This problem is extremely hard, but I'll try to help you as much as I can.

AngeI:

I mean i know you can isolate the variable but like i didnt know if thats what they had to do

mhchen:

We are given constants, 13, 5, and 36. I think we can all agree, without much controversy, that these fall within the category of natural numbers. However, is addition closed under the set of natural numbers? Yes it is, because as you can see, the lowest number of the set of natural numbers is 1, and 1+1 is 2, and 2 is also in the set of natural numbers. If we take 1+2, it becomes 3, and that is also under the set of natural numbers. Hence 2+1 is also under the set of natural numbers because by the additive commutative property of equality, a+b=b+a. We've shown that it's true for numbers 1, and 2. But what about all elements of natural numbers? Assume that n +n is a natural number, then consider n + (n+1). n+(n+1) is equal to (n+n)+1 by the additive associative property of equality. And as you can see, by our assumption (n+n) is closed under addition, and since any natural number added by 1 is also a set of natural numbers, we've shown that all natural numbers are closed under addition. Now you will see, we can rewrite the equation Y + 13 + 5 = 36 as Y + (13+5)=36 by the additive associative property of equality. Since the set of all natural numbers are closed under addition, as we've proven before, 13+5 must equal to 18. Now we have Y + 13 = 36. However now we have a problem. We don't know if subtraction is closed under natural numbers. In fact it doesn't. Consider what happens if you subtract 13 from 5? It doesn't become a natural number anymore, and they're both natural numbers! Therefore we can't assume that Y is a natural number, and we must extend it to the possibility that Y is an integer. But is the set of integers closed under addition? We are not yet smart enough to show this, so we will assume our answer is correct under the pretense that subtraction is closed under the set of integers. Then you will see, we can use the subtraction property of equality to subtract 18 by both sides of the equation, so Y + 18 - 18 = 36 - 18, and then you will see, by the associative property of equality, we can rewrite this as Y + (18-18) = 36 - 18. We know that any number minus itself is equal to 0. Therefore 18 - 18 is 0, and Y + 0 = 36 - 18. And from the zero additive property of equality, any number added by 0 is equal to that number, therefore Y + 0 = Y. And now you will see, Y = 36 - 18. All we have to do now is simplify the right-hand-side of the equation, such that Y = 18. Now remember, our solution is under the assumption that subtraction is closed under the set of integers. We have yet to prove or disprove this statement, so our solution is rather incomplete, but nonetheless, it suffices for now because your math teacher probably doesn't care about you.

AngeI:

Ily

CoolRekterizer:

That just makes it too hard, its simple. All you have to do is to grab 36 and subtract the two numbers, both 13 and 5, making 18. 36 - 18 = 18. Y = 18. Its simple...

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