My maths teacher at school showed me this, it's quite interesting, but it is NOT true. Try and spot the deliberate mistake. Try to resist the temptation to look at other people's answers.
Let y = 1
Multiply both sides by y:
y² = y
Subtract 1 from both sides:
y² - 1 = y - 1
As you would realise, the difference of two squares can be applied to the left hand side of the equation (y² and 1 are both square numbers) so, dividing both sides by (y - 1) will give:
(y² - 1)/(y - 1) = (y - 1)/(y - 1)
(y - 1)(y + 1)/(y - 1) = (y - 1)/(y - 1) because (y² - 1) = (y - 1)(y + 1) when factorised according to the difference of 2 squares.
(y + 1) = 1
y + 1 = 1
Therefore:
y = 0
Substitute y = 1 back into the above equation:
1 = 0
! !!
When my maths teacher first showed me this, I was completely baffled, but then I figured it out.
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There are 3 types of people: Those who CAN count and those who CAN'T count.
Last edited by m91 on 03 Jan 2008, 5:18 pm, edited 1 time in total.