Prove 1-n^2>0, Then 3n-2 is Even | Math Homework Help

[bonfire09]

Homework Statement

Let nεZ,Prove that 1-n^2>0, then 3n-2 is an even integer.

Homework Equations

The Attempt at a Solution

I proved it like this. I think its right but I am not able to word it correctly.

Since 1-n^2>0 therefore n=0. Then 3n-6=3(0)-6=-6. Since 0 is an integer, 3n-6 is even.

How can I learn to word this correctly because I am having some trouble with it?

 

[Whovian]

Try posting in the number theory forum, this isn't really calculus.

 

[bonfire09]

this is intro to proofs actually. I am trying to self study.

 

[Whovian]

Then this belongs in https://www.physicsforums.com/forumdisplay.php?f=155

 

[Reptillian]

I wouldn't worry too much about proper wording as long as you get the concept. n has to equal zero and -6 is an even integer...sounds proved to me. :)

Although, you probably shouldn't take my advice. I'm shunned by many in academia due to my deep detestation of pretentiousness. ;)

 

[Mark44]

Homework Statement

Let nεZ,Prove that 1-n^2>0, then 3n-2 is an even integer.

The above is confusing. A better statement would be
Let n $\in$ Z. If 1 - n² > 0, then show that 3n - 2 is an even integer.

The Attempt at a Solution

I proved it like this. I think its right but I am not able to word it correctly.

Since 1-n^2>0 therefore n=0. Then 3n-6=3(0)-6=-6. Since 0 is an integer, 3n-6 is even.

How can I learn to word this correctly because I am having some trouble with it?

Note that you have a typo in your work. You're supposed to prove that 3n - 2 is an even integer.

I would say it like this:
Since 1 - n² > 0 and n $\in$ Z, then n = 0.
So 3n - 2 = - 2, which is an even integer.

Therefore, for any integer n, if 1 - n² > 0, then 3n - 2 is an even integer.

Try posting in the number theory forum, this isn't really calculus.

It should NOT be posted in the number theory section. That section and the other sections under Mathematics are not for homework and homework-type problems

Then this belongs in https://www.physicsforums.com/forumdisplay.php?f=155

No, here is probably fine, although the Precalc Mathematics section would also be a good choice.