If you are tired of feeling broke all the time, here is some algebra that will cheer you up.
Let m be the amount of money that you actually have now,
and let n be the amount of money that you think you need.
A, their average, is given by
A = (m + n) / 2, as usual.
Now, follow this argument and see how much better you feel.
m + n = 2A
Multiply both sides by (m – n).
(m + n)(m – n) = 2A(m – n),
m2 – n2 = 2Am – 2An.
m2 – 2Am = n2 – 2An,
Now, add A2 to both sides.
m2 – 2Am + A2 = n2 – 2An + A2.
Thus (m – A)2 = (n – A)2.
So (m – A) = (n – A), and then m = n.
So you have all the money you need.
Isn’t mathematics wonderful? But how can this be? Can you find a flaw with this reasoning?
|A =||m + n||, so (m – A) = m –||m + n||=||m||–||n||=||m – n||< 0.|
|But n – A = n –||m + n||=||n||–||m||=||n – m||> 0|