Quick question on Mathematical Induction

[Residual]

In mathematical Induction, sometimes two variables are given, such as:
"All positive integers n and all real numbers x >= -1."

My question is do you solve this normally and just keep x as itself or do you have to expand it like you do with n, making it k + 1 etc etc.

Thanks in advanced

 

[Crosson]

You leave $x$ as it is, it is an arbitrary real number >= -1. In the proof it is like that you will need the fact x >= -1.
A little more context would help, but if I am guessing your issue correctly the answer is no.

 

[Residual]

Well an example would be:

|x^n| = |x|^n for every positive integer n and real number x.

 

[ZioX]

You show for any given n, x works.

Which kind of makes sense, don't you think?

 

[Residual]

I have done a few examples and they all worked nicely.

Thanks.