Prove that between any two consequtive numbers there is a number

If you multiply the two numbers together and then you divide the larger number by the smaller number you are sure to get your proof :)

Don't think that's it - it would simply return the larger intial number. But think about what you get if you calculate the average of the two numbers. By the way, the phrasse "two consecutive numbers" is curious - you can have two consecutive integers, and you can have consecutive numbers among a finite set of numbers, but there really are no "consecutive" numbers among the infinite set of all real numbers. I think the problem would be better stated as "prove that in between any two nonequal numbers there is always at least one other number."