Is 0 a positive or negative integer ?

Question

We all know that 0 is an integer. But is it postive or negative ? Interesting enough, whenever we want to indicate a postive number, we use the symbol ">". For example, m > 0 clearly implies that it is postive. Going by this definition strictly and since 0 is NOT > 0, do we conclude that 0 is not postive ? Using the similar token for definition of negativity (i.e. < 0), it seems logical to say that 0 is not negative. Then what is 0 ? Postive or Negative ? Or shall we put aside 0 as a category of its own kind ?

Answer 1

It's neither. Zero is not negative, nor is it positive. It's its own category, if you like.

Note that non-negative numbers include zero and positives. Likewise, non-positives include zero and negative numbers.

Answer 2

In mathematics, a natural number is either a positive integer
(1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...).
The former definition is generally used in number theory, while the latter is preferred in set theory and computer science.
The main thing to remember in Calculus is that you cannot divide by zero.
Whenever you have zero in the denominator this is called a
"Discontinuity".

Answer 3

Zero is neither positive, nor negative. Real analysis is riddled with errors and contradictions. Most of our mathematicians (especially the last two centuries) were not very smart. They tried hopelessly to develop a sound means of explaining calculus and the real numbers. The fact that 0.999... is supposedly equal to 1 and 0 is neither +ve or -ve is clearly contradictory. And what is infinitesimal but a vague and hazy notion that has never been well-defined? Break away from the common erroneous paradigms - begin to think for yourself!

rgetso: Even the "little" you claim to know is questionable, never mind rock-solid...

Answer 4

Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5, ... . Negative integers are all the opposites of these whole numbers: -1, -2, -3, -4, -5, … . We do not consider zero to be a positive or negative number. For each positive integer, there is a negative integer, and these integers are called opposites. For example, -3 is the opposite of 3, -21 is the opposite of 21, and 8 is the opposite of -8. If an integer is greater than zero, we say that its sign is positive. If an integer is less than zero, we say that its sign is negative.

Answer 5

I think your argument answered your question in a very nice way. You've shown that zero is not positive and you've also shown it is not negative. Well, you only have two possibilities. But, by your reasoning, you have developed a third. Therefore, zero is neither positive nor negative. It's ZERO.

Now, I'm not sure what Tom is thinking. Our current day mathematicians are brilliant beyond belief. I believe real analysis is on a firm foundation and will continue to stand the test of time. I'm not so sure about obvious errors and/or contradictions. However, I am no real analysis expert by any means, but the little I am aware of is rock solid. No, it's titanium solid!

Answer 6

Zero is a neutral number - neither positive or negative. You could define zero as its own category, and it would be the only value in its category. Think of the x-y coordinate system. On the x-axis, numbers on the right side of the y-axis crossing are positive, while numbers on the left side of the y-axis crossing are negative. However, the number at which the y-axis crosses the x-axis, zero, is neither negative nor positive - hence, neutral, or in other words, uncharged.

Answer 7

It's neither positive or negative.

I find it interesting, that when dealing with inequalities, if you multiple by a positive number you don't change the comparator.
x > 5
2x > 10

If you multiple it by a negative you flip the comparator
x > 5
-2x < -10

But if you multiply be zero, you must change the comparator to an equals.

x > 5
0x = (0)(5)

Answer 8

It's neither... I thought positive #s were anything more than 0, and negatives anything less than 0.

Isn't 0 more of a reference point, then?

Answer 9

Is 0 a positive integer or a negative integer? No.

Answer 10

Zero is neither positive nor negative, neither a prime number nor a composite number, nor is it a unit.