The above is confusing. A better statement would bebonfire09 said:Homework Statement
Let nεZ,Prove that 1-n^2>0, then 3n-2 is an even integer.
Note that you have a typo in your work. You're supposed to prove that 3n - 2 is an even integer.bonfire09 said: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?
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 problemsWhovian said:Try posting in the number theory forum, this isn't really calculus.
No, here is probably fine, although the Precalc Mathematics section would also be a good choice.Whovian said:Then this belongs in https://www.physicsforums.com/forumdisplay.php?f=155
In order to prove that 1-n^2 > 0, we can use the fact that n^2 is always greater than or equal to 0. This means that when we subtract n^2 from 1, the result will always be greater than 0.
A number is considered even if it is divisible by 2 without leaving a remainder. In the case of 3n-2, this means that the value of the expression will always be a multiple of 2.
In order to prove that 3n-2 is even, we can use the fact that any integer multiplied by an even number will always result in an even number. Since 3 is an odd number, the remaining number in the expression (n-2) must be even for the whole expression to be even. And since n-2 is even, this means that 3n-2 is also even.
No, we cannot use a counterexample to disprove the statement. The statement is a conditional statement which means that it is true for all possible values of n. A counterexample would only disprove the statement if it is not true for all values of n, but in this case, the statement is true for all values of n.
The initial statement, 1-n^2 > 0, serves as a premise or condition for proving that 3n-2 is even. By showing that 1-n^2 is always greater than 0, we can then use this information to prove that 3n-2 is always even.