Is Zero Even? - Numberphile
video description
My understanding is that it isn't, but a useful concept to signify the crossing point between positive and negative. It doesn't have the basic quality of ALL other numbers, being totally dimensionless in a one dimensional system. This suggests it isn't part of this system, and is not a number. Therefore is a concept. The question of it being even, positive or negative is therefore meaningless.
n / 0 = infinity. Using the explanation from the root 2 video would suggest it would at least be irrational. As zero has no dimension, to divide by it is logically impossible, there's nothing to divide by.
To get infinity is incorrect. (remember the schoolboy 'proof' that 0=infinity) it is NOT infinitely small, that's the cheat to give it a dimension and therefore make it a number, and would therefore require polarity. Therefore the equation has no meaning.
Are we perhaps so familiar with zero that we ignore it's inconsistencies and avoid the question?
That's my understanding, so tell me why I'm wrong.
Date: 2022-04-08
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Comments and reviews: 9
Lt.
You claim that zero is CATEGORICALLY an even number because it fits every definition of an even number. But when you go through all the definitions of an even number and get to the part where even numbers can be divided against themselves to get one, you just kind of gloss over it and pretend it doesn't matter. That's the problem I have with mathematicians. You make up rules and claim these rules are absolute but then, when you come to an exception to the rule, you just ignore it and pretend it doesn't exist. It does exist. You can't divide zero by zero and get one. Therefore, it's NOT an even number. Zero is a neutral number; Neither odd nor even; Neither positive nor negative.
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You claim that zero is CATEGORICALLY an even number because it fits every definition of an even number. But when you go through all the definitions of an even number and get to the part where even numbers can be divided against themselves to get one, you just kind of gloss over it and pretend it doesn't matter. That's the problem I have with mathematicians. You make up rules and claim these rules are absolute but then, when you come to an exception to the rule, you just ignore it and pretend it doesn't exist. It does exist. You can't divide zero by zero and get one. Therefore, it's NOT an even number. Zero is a neutral number; Neither odd nor even; Neither positive nor negative.
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bitcoin
Lol. zero = nothing. a human concept of absence. a concept that in our reality is untrue. there is something, there has to be something, or we wouldn't be having this interaction. Unless this is my imagination amd really I am just interacting with myself. Nothing /2 = Nothing( your imagination. 0 x 2 = Nothing( your imagination) and so on. Just because we use a concept(designated by a symbol 5(0) ) the 0 in 50 does not represent the same. i. e. Nothing. 0. thats a strawman to fir your understanding. but is obviously logical false in reality. because 50 represents something tangible
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Lol. zero = nothing. a human concept of absence. a concept that in our reality is untrue. there is something, there has to be something, or we wouldn't be having this interaction. Unless this is my imagination amd really I am just interacting with myself. Nothing /2 = Nothing( your imagination. 0 x 2 = Nothing( your imagination) and so on. Just because we use a concept(designated by a symbol 5(0) ) the 0 in 50 does not represent the same. i. e. Nothing. 0. thats a strawman to fir your understanding. but is obviously logical false in reality. because 50 represents something tangible
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Hugh
I may have missed the point, but what is 0x1? 0 divided by 1? That part of your explanation eluded me, I'm afraid. It would suggest to me that 0 is both even and odd. Or, neither even or odd ( which -feels- like the answer)
Thoughts, anyone?
Also it would seem that even preliterate merchants would have some concept of zeroness: - How much for a sheep? They are one ducat each. I'll take five, please. here's a five ducat coin. how much change might I expect? Zero, of course-
That seems numerical, doesn't it?
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I may have missed the point, but what is 0x1? 0 divided by 1? That part of your explanation eluded me, I'm afraid. It would suggest to me that 0 is both even and odd. Or, neither even or odd ( which -feels- like the answer)
Thoughts, anyone?
Also it would seem that even preliterate merchants would have some concept of zeroness: - How much for a sheep? They are one ducat each. I'll take five, please. here's a five ducat coin. how much change might I expect? Zero, of course-
That seems numerical, doesn't it?
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Rex
Do we really believe that nobody thought of things like -how many times did the bucket fill up with rainwater today? - until the seventh century CE? Considering the obsession that many ancient folk had with tracking and recording seasonal events, it seems unlikely to me.
I know that different definitions of even and odd are equivalent, but I would suggest that -even numbers leave a remainder of 0 when divided by 2; odd numbers leave a remainder of 1- would leave nobody with any doubt about the evenness of zero.
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Do we really believe that nobody thought of things like -how many times did the bucket fill up with rainwater today? - until the seventh century CE? Considering the obsession that many ancient folk had with tracking and recording seasonal events, it seems unlikely to me.
I know that different definitions of even and odd are equivalent, but I would suggest that -even numbers leave a remainder of 0 when divided by 2; odd numbers leave a remainder of 1- would leave nobody with any doubt about the evenness of zero.
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Noah
Also, algebraically, an odd number is a number that gives a whole number when doubled and minus or add 1:
2n-1 is odd, and so is 2n+1
Let's say, for 0 to be odd
2n - 1 = 0
2n = 1
n = 1/2,
but because n in this case isn't a whole number, in fact halfway between, 0 can't be odd, so is even.
Moreover, using the same calculation, an even number will always be something and a half, for example
2n - 1 = 2
2n = 3
n = 1 and 1/2
2n + 1 = 10
2n = 9
n = 4 and 1/2
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Also, algebraically, an odd number is a number that gives a whole number when doubled and minus or add 1:
2n-1 is odd, and so is 2n+1
Let's say, for 0 to be odd
2n - 1 = 0
2n = 1
n = 1/2,
but because n in this case isn't a whole number, in fact halfway between, 0 can't be odd, so is even.
Moreover, using the same calculation, an even number will always be something and a half, for example
2n - 1 = 2
2n = 3
n = 1 and 1/2
2n + 1 = 10
2n = 9
n = 4 and 1/2
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Michael
You forgot one.
Numbers ending in zero are even.
For instance, 10, 20, 15, 000, etc. Whereas 14999 is odd, and 15001 are odd, 15000 is even.
So, IMO, in that sense, it also satisfies -even-ness, - just as do other numbers that end in -even- digits: 16, 28, 32, 44, etc. If 0 were odd, then something like 500 would have to be odd since it ends in an odd number, and then you'd have 3 odd numbers in a row, which would seem nonsensical.
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You forgot one.
Numbers ending in zero are even.
For instance, 10, 20, 15, 000, etc. Whereas 14999 is odd, and 15001 are odd, 15000 is even.
So, IMO, in that sense, it also satisfies -even-ness, - just as do other numbers that end in -even- digits: 16, 28, 32, 44, etc. If 0 were odd, then something like 500 would have to be odd since it ends in an odd number, and then you'd have 3 odd numbers in a row, which would seem nonsensical.
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Lt.
Why does zero have to be odd or even? Why are we forcing zero to pick a side? Why can't zero be neutral? Neither positive nor negative; Neither odd nor even. It's just zero. Zero is a number category all by itself. In order to be a number, it has to fit into the rules of every other number. Zero does not. You can divide any number, except zero, by any other number. You can't divide zero by zero. If the number don't fit, you must acquit.
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Why does zero have to be odd or even? Why are we forcing zero to pick a side? Why can't zero be neutral? Neither positive nor negative; Neither odd nor even. It's just zero. Zero is a number category all by itself. In order to be a number, it has to fit into the rules of every other number. Zero does not. You can divide any number, except zero, by any other number. You can't divide zero by zero. If the number don't fit, you must acquit.
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Lt.
Zero is neither odd nor even BECAUSE it is neither positive nor negative.
-It will follow every definition of an even number. - It will not.
-Every even number can be divided by two- EVERY number is divisible by 2. Every number is also divisible by zero. except zero. While zero can be divided by 2, every even number divided by itself is 1. You can't divide zero by zero.
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Zero is neither odd nor even BECAUSE it is neither positive nor negative.
-It will follow every definition of an even number. - It will not.
-Every even number can be divided by two- EVERY number is divisible by 2. Every number is also divisible by zero. except zero. While zero can be divided by 2, every even number divided by itself is 1. You can't divide zero by zero.
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Douglas
-an even number is something time 2- hmm, a half is something, 1/2 x 2 = 1, 1 I believe is odd.
-divisible by 2-, 2/3 divided by 2, is 2/3 an even number? Are any fractions odd or even?
is the rule for odd and even only for real, whole numbers?
And by the way O (oh) is not zero, a phone number 9500 is not Nine five oh oh. Oh on your phone keyboard is 6.
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-an even number is something time 2- hmm, a half is something, 1/2 x 2 = 1, 1 I believe is odd.
-divisible by 2-, 2/3 divided by 2, is 2/3 an even number? Are any fractions odd or even?
is the rule for odd and even only for real, whole numbers?
And by the way O (oh) is not zero, a phone number 9500 is not Nine five oh oh. Oh on your phone keyboard is 6.
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