And what if we don't achieve our dreams?

"If A then B" is logically equivalent to "If (Not B) then (Not A)". For example "if a shape has three sides, then it is a triangle" is logically equivalent to "if a shape is not a triangle, then it does not have three sides". The second statement in quotes is called the contrapositive of the first statement in quotes. Logically speaking, they are identical statements. If one is true, the other must be, and vice versa. In this case, they are both true statements.

A commonly touted inspirational message we deliver to young people can be distilled down to "if you do all the things right that are within your power, then your dreams will come true". Consider its contrapositive. 

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