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Fri 25 Jun, 2004 11:12 pm
Suppose you have two numbers: x and y
x < y
Now, suppose x and y are two random numbers. Will x eventually be half of y if you had a certain amount to each side? And will it only happen once? Does this apply to any two numbers?
For example:
x = 10
y = 25
You add 5 to both sides. so now that x = 15 and y = 30 and now x = 1/2y
And if you add a certain amount of number to each side again, will x ever be half of y again?
Is there a proof for this?
Not if x is more than 1/2y to start with
Well, in that case, whatever equation you use to add to the two numbers, you would subtract instead of add, correct?
Proof (allowing the addition of negative numbers):
Let D be the difference between X and Y (D=Y-X).
So, start with X and Y.
X, Y
Add D-X to both
X+D-X, Y+D-X
Simplify the left side and rearrange the right side
D, Y-X+D
Substitute D for Y-X on the right side
D, D+D
The right side is now twice the left side
The difference between the right and left sides will always be D (as long as you add the same number to each side) so there is only one way to get to the state where the new Y is twice the new X. That is when X=D.
Another way to prove it.
Assume D = the number we add to X to make it (1/2)Y
We need to prove a number D exists so that
X + D = .5 * (Y + D)
Simplify
2X + 2D = Y + D
D = Y - 2X
In the example D = 25 - 2 * 10 = 5
will your children ever be older than you?
BoGoWo wrote:will your children ever be older than you?
maybe... if you die at 50 and your children live past that, you could consider them older than you... maybe
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