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Simplify This!

Simplify This!

Posers and Puzzles

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Simplify the following exercise in multiplication as much as possible:

(x+a)(x-b)(x+c)(x-d)...(x-z)

Please hide your explanation, especially if you have seen the solution.

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0

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Very good. Didn't get it straight away. 😞 (Maths degree)

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Originally posted by wolfgang59
Very good. Didn't get it straight away. 😞 (Maths degree)
Wouldn't that depend on a multiplication being a zero? I mean, what if X=28 and a=0, b =1, c=2, etc.? Where would there be a zero multiplicand result?

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Originally posted by sonhouse
Wouldn't that depend on a multiplication being a zero? I mean, what if X=28 and a=0, b =1, c=2, etc.? Where would there be a zero multiplicand result?
One of the items in the series is (x-x)...

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Originally posted by bbarr
One of the items in the series is (x-x)...
Yeah, that would do it🙂

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except if x = +- infinity, when the answer is undefined

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Originally posted by iamatiger
except if x = +- infinity, when the answer is undefined
Is infinity minus infinity undefined?

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Originally posted by iamatiger
except if x = +- infinity, when the answer is undefined
as x --> infinity, x - x = what?

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Originally posted by iamatiger
except if x = +- infinity, when the answer is undefined
infinity is a symbol not a number, so x can't equal infinity...Even the lim(x->infinity) doesn't yield any kind of problem.

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Infinity - Infinity is undefined, as with an infinite number of hotel rooms I can either put an infinite number of guests in every room, having zero free rooms, or I can put an infinite number of guests in every second room, having an infinite number of free rooms, or I can miss out any finite number of rooms at the start, and still fit my guests in with that finite number of rooms left.

I think claiming infinity is a symbol and not a number is rather dodgy. All numbers are symbols too, and infinity comes up in valid mathematics. If you are worried about saying x=infinity, then let us define x=1/0

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Originally posted by iamatiger
Infinity - Infinity is undefined, as with an infinite number of hotel rooms I can either put an infinite number of guests in every room, having zero free rooms, or I can put an infinite number of guests in every second room, having an infinite number of free rooms, or I can miss out any finite number of rooms at the start, and still fit my guests in with t ...[text shortened]... es up in valid mathematics. If you are worried about saying x=infinity, then let us define x=1/0
So pretending, we have x = 1/0.

What is 1/0 - 1/0?

Multiply both sides by 0. Eliminates the 0's.

We have 1-1.*

What is 1-1?

0.

Ergo, x-x=0 even when x=1/0 in the pretend world.

*Edit: or we have 0-0 at the starred equation. Same outcome.

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😉
multiplying both sides by 0 just proves 0=0 (as 0 converts everything to 0)

4 = 5
multiply both sides by 0
0 = 0

0/0 is undefined too, by the way

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Originally posted by iamatiger
except if x = +- infinity, when the answer is undefined
x-y may be undefined where both x and y ->inf but x-x ???

It is zero, even when x->inf