Maybe stupid question - zero positive or negative ?

[JPC]

Homework Statement

Hi
I have to say true or false, and then demonstrate my answer
"if taking any 3 Real numbers (a, b, c), we have at least 2 of the same sign"

For me its true, i was thinking of creating a triplet (x, y, z), where
x=1 if "a" positive, x=0 if "a" negative, same for y, and z
and show that with the all the (x, y, z) possibilities, you had always 2 of the same sign

But then, i realized, what if one of the reals a, b, c is equal to 0 ?
like if (a, b, c) = (0, 0, 0)

Is zero considered positive or negative, or both ?

If so, i would have to add another value to the reals of the (x, y, z) triplet , 2, which i can then take as positive when i need or as negative when i need

 

[Mark44]

Zero is neither positiive nor negative.
Any real number that is positive is greater than zero, and any negative real number is less than zero.

 

[JPC]

ok thank you
then i must reply false to the proposition "if taking any 3 Real numbers (a, b, c), we have at least 2 of the same sign", because with (0, 0, 0) for example , we have none of the same sign

 

[Mark44]

ok thank you
then i must reply false to the proposition "if taking any 3 Real numbers (a, b, c), we have at least 2 of the same sign", because with (0, 0, 0) for example , we have none of the same sign

Right. Another example is (1, 0, -1).

 

[JPC]

ok, thank you, you helped me save time not doing a long and incorrect maths demonstration :)

 

[HallsofIvy]

ok thank you
then i must reply false to the proposition "if taking any 3 Real numbers (a, b, c), we have at least 2 of the same sign", because with (0, 0, 0) for example , we have none of the same sign

No. 0 is neither positive nor negative but is "its own sign". A better example is (-1, 0, 1).

 

[JG89]

0 is non-negative.

 

[HallsofIvy]

0 is non-negative.

Which does not answer the question (which had already been answered). 0 is also non-positive.

 

[Gr!dl0cK]

As others have already said, 0 is neither. 0 is basically the line between positive and negative.
:)