Is zero really a number?

If it is, why is it so different from any other number? Adding or subtracting it from any other number does nothing. Multiply any other number by zero, and the answer is always zero. Early calculators used to indicate an error when you tried dividing by zero, but not any other number.
Why were the Romans able to rule their known world without the use of zero? They managed without a zero but couldn't do much without any of the other nine numbers.
The other nine numbers all follow set rules, but zero follows a different set. Most of the time, it functions as a normal number, but sometimes it, and only it, can go rogue.
Is zero the Pluto of numbers?

On a number line, zero is the number between 1 and -1. So if you believe in negative numbers (which you might not) then you must accept zero as a number.

There are many, many internet sites on this subject.

It is like asking whether 1 should be considered a prime number - if the definition of prime number should be changed by extending it to include 1.

Zero's properties where multiplying it by anything also yields zero, and dividing anything by it can't be done at all, are the whole point!

We all learned to appreciate the multiplicative property back in freshman algebra class, where you get a zero on one side of an equation and a bunch of factors on the other side, and you know at least one of those factors has to be zero. Back then I recognized solving that class of equation would be a lot harder if you couldn't do that. 5-7 years later in your differential equations class you'll be doing things that remind you of that too. But there was no algebra until the 9th century so it wasn't until well after the fall of Western Rome that they needed a zero.

In physics the property of zero where you can't divide by it is how you identify things that are wrong. Anything bad, evil, "non-physical," false, problematic, cannot exist etc. will have in it or lead in some way to a division by zero. The most fundamental of those is the Einstein & Lorentz Special Relativity equations where you have a term of sqrt(1-v²/c²) in the denominator, where c is the speed of light in vacuum and v is your velocity, and if they are both equal it's 1-1, which is zero, and you can take the square root of that and that's fine, that's also zero, but now it's in the denominator so you're screwed. That proves that there is no such thing as any real thing having a velocity of c. We didn't know it, but back in third grade when we were learning division and were told "Division by zero does not exist" we thought it was just another silly rule, but we had no idea that these really smart guys were basing their whole description of physical reality on the fact that it doesn't exist.

All I can add is it was Christmas a few years back. Some relative insisted a number divided by zero is zero.

I got about 9 cookies and said.....

"Put those in equal piles of zero with none left over."

Eventually we ate the cookies.

Saved By Zero...

You can have negative numbers, but not negative zero.

Shouldn't it be 3,2,1 0,-0,-1, -2.....

1 and -1 are very different and not at all interchangeable. Negative zero, if it exists, has the exact same principles as zero. If it doesn't exist, it is yet another difference from the other nine

All indications are that zero was added much later than the other nine numbers and didn't get used in Western Europe until after the Crusades.
Another interesting factoid- zero seemingly developed in India and Central America almost at the same time, after the original nine numbers had been in use for over a thousand years.

Sometimes I walked past the bank sign in the middle of the night and it would say it was -0 degrees outside. I'm assuming that was rounded up from -0.4 through -0.1.

Quote: billryan

Why were the Romans able to rule their known world without the use of zero? They managed without a zero but couldn't do much without any of the other nine numbers.
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Well, the Romans certainly understood the concept of the digit zero. Didn't most Romans use a base-10 abacus for calculations?

As for not needing zero, it certainly made things messy, especially with years - when they had to count the number of years from "before {something}" to "the year of {that same thing}," they couldn't just add up the two numbers.

Quote: gordonm888

...It is like asking whether 1 should be considered a prime number - if the definition of prime number should be changed by extending it to include 1.
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I was taught that 1 is prime! It has to do with your age and the age of your teachers and your/their textbooks. And it works for the grade school definition of prime numbers, where it's almost like trivia and it doesn't break anything if you call 1 prime. It isn't until later in education and the practical uses of prime numbers where calling 1 prime doesn't work, it has to be excluded.

Quote: ThatDonGuy

Quote: billryan

Why were the Romans able to rule their known world without the use of zero? They managed without a zero but couldn't do much without any of the other nine numbers.
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Well, the Romans certainly understood the concept of the digit zero. Didn't most Romans use a base-10 abacus for calculations?

As for not needing zero, it certainly made things messy, especially with years - when they had to count the number of years from "before {something}" to "the year of {that same thing}," they couldn't just add up the two numbers.
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There is no Year Zero. The day after December 31, 1BC was January 1, 1 AD.
I had no idea Romans used an abacus. I thought they were an Asian instrument.

According to the NFL, zero has been a number since 2023.

Quote: billryan

You can have negative numbers, but not negative zero.

Shouldn't it be 3,2,1 0,-0,-1, -2.....

1 and -1 are very different and not at all interchangeable. Negative zero, if it exists, has the exact same principles as zero. If it doesn't exist, it is yet another difference from the other nine

All indications are that zero was added much later than the other nine numbers and didn't get used in Western Europe until after the Crusades.
Another interesting factoid- zero seemingly developed in India and Central America almost at the same time, after the original nine numbers had been in use for over a thousand years.
link to original post

-n is -1 times n. If n=0, -n=-1x0=0.

So they are the same which is why the number line can be written as 3, 2, 1, 0=-0, -1, -2, -3, etc. 7 entries from 3 down to -3, not 8.

If you have 1 and subtract 1 you have 0. If there was no 0 you would not have zero coke, it would just be coke.