A number decreased by itself is greater than the number, but what is the number?

Question

I've tried dividing through by the number, but I just get 0>1 , I don't understand how that is possible.

Answer 1

Hi Asked,

An excellent way to demonstrate how you can go astray in even simple algebra problems!

You had:

x - x > x and you did /x to get:

1 - 1 > 1

0 > 1

You should instead have simplified on the left side of the inequality:

x - x > x

0 > x

x < 0

Then the solution is simple, isn't it.

Division and multiplication can lead you astray, if you do not mark down your assumption that x>0 as you preserve your inequality. If you had marked it down, then you would go back and revisit that assumption, when you got your non-sensical 0 > 1 result.

In the same vein, if you needed to split your calculation into two branches in order to solve each, then you'd need to go back and check that your assumption(s) were correct, when you obtained your tentative solution(s). Otherwise, your results may be trash!