What Is The Meaning Of 0 In Math?

[caprija]

In a whole number you can say whether it's negative or positive right?

So what would you call 0?

would it just be called zero?

 

[Hurkyl]

0 is nonnegative and nonpositive, and it is the only such integer.

 

[caprija]

0 is nonnegative and nonpositive, and it is the only such integer.

so is there a term for it??

I have to make a computer program that outputs whether the number is positive or negative, so when the user enters zero what should it output?

 

[Galileo]

A blue screen with fatal exception error, followed by automatic reboot.

 

[caprija]

A blue screen with fatal exception error, followed by automatic reboot.

but shouldn't the program output a different term when the number zero is typed in?

 

[mattmns]

Why not just have the program output: "0 is neither positive nor negative"

 

[StatusX]

You could have the user ask "Is x positive or negative?" and when x is 0, instead of saying "positive" or "negative", just say "no".

 

[hypermonkey2]

You could have the user ask "Is x positive or negative?" and when x is 0, instead of saying "positive" or "negative", just say "no".

So it would be sort of like the boxer/briefs paradox?

 

[StatusX]

So it would be sort of like the boxer/briefs paradox?

Yea, same idea. Although I'm less troubled by the fact that 0 is neither positive or negative.

 

[shmoe]

"0 is going commando" seems like the appropriate output.

 

[HallsofIvy]

I have to make a computer program that outputs whether the number is positive or negative, so when the user enters zero what should it output?

A blue screen with fatal exception error, followed by automatic reboot.

but shouldn't the program output a different term when the number zero is typed in?

It was a joke, son, a joke! (And, in my opinion, a good one.)

I would vote for responding "neither".

 

[arildno]

So it would be sort of like the boxer/briefs paradox?

Exactly!
It is what is INSIDE that is important; externals like the labels "positive/negative" are unimportant stuff.

 

[Robokapp]

but shouldn't the program output a different term when the number zero is typed in?

It would probably output something along the lines of this:


http://i3.photobucket.com/albums/y100/Robokapp/untitledfff.jpg

But honestly, although it should stay blank, it will...probably say something. I mean let's look at it this way, it's a positive thing to have zero debts, but it's negative to have zero income...I guess it's up to the maker's financiar life...

This should be in the psychology section.

 

[-Job-]

If the computer is using signed 2's Complement for number representation, then 0 will interpreted as a positive. Negative numbers would be the ones where the most significant bit is 1. Thus, 0 would be positive.
Some number representations have both a negative 0 and a positive 0, for example. But signed 2's complement is a popular representation, and your best bet is that 0 is a positive number, if this is for a Computer Science course.

 

[Robokapp]

In all honesty I think the problem lays in the meaning of the worlds "positive" and "negative". No matter how we look at it 0 won't turn negative... because it obviously involves a missing quantity. zero is the absence of quantity so nothing can't be missing.

In mathematics, a number is called positive if its value is greater than zero. See negative and non-negative numbers.

Zero is neither positive nor negative, neither a prime number nor a composite number, nor is it a unit. If zero is excluded from the rational numbers, the real numbers or the complex numbers, the remaining numbers form an abelian group under multiplication.

Now the last part of the second quote didn't look like english to me but...i quoted the whole paragraph...

 

[Hurkyl]

it's a positive thing to have zero debts, but it's negative to have zero income

Equivocation. Your usage of those English words has absolutely nothing to do with the mathematical terms.

In all honesty I think the problem lays in the meaning of the worlds "positive" and "negative".

I assume you meant "words". Positive means bigger than zero. Negative means less than zero. What's the problem with that?

zero is the absence of quantity

No, it is not. For example, when filling out a form, there's a huge difference between leaving

Children: _____

blank (absence of quantity), and filling it in

Children: __0__

with a zero.


The only "problem" here is that natural language likes to single out small quantities linguistically. "Zero" isn't the only word with this problem: "one" also has a lot of specialized language associated with it (not to mention the different spellings required for many unspecialized words). And even "two", "three", and "four" have some specialized words associated with them.

 

[Robokapp]

Children: __Maybe__

 

[mtanti]

Positive and negative numbers are just 2 states of integers/real numbers. Then there is 0! Numbers are really in tri-state and zero is the bridge joining positives to negatives. So the output must be either positive, negative or zero.

However in computer science you are forced to accept that zero is a positive number since it is sometimes considered to be a natural number and is grouped with the positive numbers. So to conserve space of bits in registers they use just one bit (0 or 1) to describe the sign of the number instead of 2 bits (4 values) to include the zero state as well.

Is zero a natural number?

 

[radou]

No, zero is not a natural number.

 

[shmoe]

There's no universal convention on whether 0 is a natural number or not. Some authors include it, some don't.

 

[HallsofIvy]

Is the word "neither" too complicated for you?

 

[CRGreathouse]

There's no universal convention on whether 0 is a natural number or not. Some authors include it, some don't.

Doesn't that vary mostly by field, though? Number theorists say one thing, etc.

 

[Robokapp]

Is the word "neither" too complicated for you?

It's too difficult to "swallow" although it makes sense...

 

[shmoe]

Doesn't that vary mostly by field, though? Number theorists say one thing, etc.

Probably it varies much less within a given field, but it can still vary.