If X is a positive integer,then -x is a negative integer."this statement is false,what could be a possible counterexample?

Question

sshayer · Answer

if x=0 then what is -x?

agent0smith · Answer

@sshayer if x=0 then it doesn't satisfy the first condition.

agent0smith · Answer

"If x is a positive integer,then -x is a negative integer."
Seems like a true statement to me...

vheah · Answer

basically what it's saying is that if X was a number and it was positive, a -X would multiply that number by a negative so the X will become a negative number. So that statement is true.

tkhunny · Answer

X is a positive integer.
-x can easily be positive integer, or zero, or a negative integer.

"X" has nothing to do with "x".

mrnood · Answer

Maybe you have made the assumption that x is a member of the set of integers.

If x is defined as a member of the set of positive integers then -x is undefined.

@tkhunny
I see your point but I think you are being a little over pedantic even for a maths forum!

agent0smith · Answer

@MrNood in that case, you cannot provide a counter example, since one does not exist.

The question is written pretty poorly, but it's unlikely the OP will return to correct it.

tkhunny · Answer

"A little over pedantic"?  Absolutely not.  Quite deliberately excessive.

1) It never hurts to emphasize the dangers of changing horses in the middle of the stream.
2) Just trying to satisfy EXACTLY what the poorly-worded question was asking.