I learned this in 7th grade. Zero is not an integer. You cannot divide a number by zero. Try it, the calculator says ERROR. It makes me cringe when people say it's even, because it's neither. Zero is not a natural number. It's basically like a place holder, so it's not even or odd.
tony - 15 years ago
even numbers are divisible by 2 without a remainder. 0/2=0. 0 is even.
Kevin W - 15 years ago
Wow, never even thought about it. To me, 0 seems to be clearly even, as much as 2 or 4 is. N is even if N is an integer and N/2 is also an integer. Isn't this pretty much the common definition of evenness?
Practical situation: I have N cookies that I must evenly divide between my two children. What values of N will relieve me of having to carefully break 1 cookie in half to prevent one of my children from becoming upset that the other got an extra cookie? (Sure, neither of my kids would particularly like the 0 cookie situation, but they would probably be even more upset at the prospect of "unfairness").
Monte Meals - 15 years ago
@John Costello "Zero [0] is not a number at all. It is a place holder."
In a base ten counting system, the digits are:
0 1 2 3 4 5 6 7 8 9
If you omit zero (0) you are invoking a base nine (9) system with just nine digits:
1 2 3 4 5 6 7 8 9
John Costello - 15 years ago
Zero [0] is not a number at all. It is a place holder. Can you divide it by itself? What if you add up a collumn of 100 zeros? How much do they add up to: nothing at all.
Sagar - 15 years ago
The folks who think it is neither, or those who think it is both, could you please provide your rationale?
75984_62153 - 15 years ago
I give you the ultimate authority on all disputes, Wikipedia:
http://en.wikipedia.org/wiki/Evenness_of_zero
Case closed.
Marc W - 15 years ago
Jonathan Abolins:
There are other properties of even numbers for which zero does fit. E.g., the sum of two even numbers is an even number. 4+0=4, an even number.
Not sure what exactly you mean by this, Yes, the sum of two even numbers is even. But zero in no way violates that. Take, for example, your example. 4+0=0. Two even numbers (4 and 0). And the sum (4) is even.
Redman - 15 years ago
Zero is between +1 and -1, both of which are odd numbers, so zero is even.
chuck - 15 years ago
1. even numbers are those that are equal to zero, mod 2.
2. even numbers and odd numbers alternate
-3 -2 -1 0 1 2 3
o E o E o E o
Of course, this is not a logical question, it's a question of how to comply with a conventional definition. The convention can go in just about any direction.
Tamerlane - 15 years ago
This is junior high school algebra and 55% of a sample that is biased towards the highly educated and the intelligentsia gets it wrong. Even though I've recently taught at the university level, I confess that I didnt realize things were this bad.
Much depends upon how we define what's an "even" number. Usually, the definition of an even number is one that's evenly divisible by two. By this definition, zero is an even number.
There are other properties of even numbers for which zero does fit. E.g., the sum of two even numbers is an even number. 4+0=4, an even number.
Rob - 15 years ago
Zero is an even number. Apparently, some intelligent (if they are visitors to this site) did not know that.
Off Kilter - 15 years ago
Despite my answer being in the minority, I've no doubt it is correct. I didn't even perceive it as a question on which there was a controversy. My mistake as regards the latter.
Chris - 15 years ago
"Why don't we take a vote on whether the Moon is made of cheese."
Given the way this poll is trending, I have a feeling that the top answer would be "Gouda".
Paul Edelman - 15 years ago
Again, Eugene? Why don't we take a vote on whether the Moon is made of cheese.
I learned this in 7th grade. Zero is not an integer. You cannot divide a number by zero. Try it, the calculator says ERROR. It makes me cringe when people say it's even, because it's neither. Zero is not a natural number. It's basically like a place holder, so it's not even or odd.
even numbers are divisible by 2 without a remainder. 0/2=0. 0 is even.
Wow, never even thought about it. To me, 0 seems to be clearly even, as much as 2 or 4 is. N is even if N is an integer and N/2 is also an integer. Isn't this pretty much the common definition of evenness?
Practical situation: I have N cookies that I must evenly divide between my two children. What values of N will relieve me of having to carefully break 1 cookie in half to prevent one of my children from becoming upset that the other got an extra cookie? (Sure, neither of my kids would particularly like the 0 cookie situation, but they would probably be even more upset at the prospect of "unfairness").
@John Costello "Zero [0] is not a number at all. It is a place holder."
In a base ten counting system, the digits are:
0 1 2 3 4 5 6 7 8 9
If you omit zero (0) you are invoking a base nine (9) system with just nine digits:
1 2 3 4 5 6 7 8 9
Zero [0] is not a number at all. It is a place holder. Can you divide it by itself? What if you add up a collumn of 100 zeros? How much do they add up to: nothing at all.
The folks who think it is neither, or those who think it is both, could you please provide your rationale?
I give you the ultimate authority on all disputes, Wikipedia:
http://en.wikipedia.org/wiki/Evenness_of_zero
Case closed.
Jonathan Abolins:
There are other properties of even numbers for which zero does fit. E.g., the sum of two even numbers is an even number. 4+0=4, an even number.
Not sure what exactly you mean by this, Yes, the sum of two even numbers is even. But zero in no way violates that. Take, for example, your example. 4+0=0. Two even numbers (4 and 0). And the sum (4) is even.
Zero is between +1 and -1, both of which are odd numbers, so zero is even.
1. even numbers are those that are equal to zero, mod 2.
2. even numbers and odd numbers alternate
-3 -2 -1 0 1 2 3
o E o E o E o
and so on.
Chuck
Of course, this is not a logical question, it's a question of how to comply with a conventional definition. The convention can go in just about any direction.
This is junior high school algebra and 55% of a sample that is biased towards the highly educated and the intelligentsia gets it wrong. Even though I've recently taught at the university level, I confess that I didnt realize things were this bad.
Much depends upon how we define what's an "even" number. Usually, the definition of an even number is one that's evenly divisible by two. By this definition, zero is an even number.
There are other properties of even numbers for which zero does fit. E.g., the sum of two even numbers is an even number. 4+0=4, an even number.
Zero is an even number. Apparently, some intelligent (if they are visitors to this site) did not know that.
Despite my answer being in the minority, I've no doubt it is correct. I didn't even perceive it as a question on which there was a controversy. My mistake as regards the latter.
"Why don't we take a vote on whether the Moon is made of cheese."
Given the way this poll is trending, I have a feeling that the top answer would be "Gouda".
Again, Eugene? Why don't we take a vote on whether the Moon is made of cheese.