Is zero an even number?

Quote: JyBrd0403

Perhaps, it's better I directly ask the question. When you use the "number" 0, are you using a "number" to denote the absence of numbers (value, quantity)?

No. Zero is a number as much as any other integer. There is no expression that I know of for a void of a number at all.

The closest thing I can think of is in computer programming where if you don't declare what a variable is, then in English you would say it is "undeclared." If you ask to see the variable, it will show whatever number was last left in that part of the computers memory. At least in C++. A good compiler will warn you about using uninitialized variables, a source of many bugs. Sorry, this going off on a tangent a bit.

Quote: Wizard

No. Zero is a number as much as any other integer. There is no expression that I know of for a void of a number at all.

The closest thing I can think of is in computer programming where if you don't declare what a variable is, then in English you would say it is "undeclared." If you ask to see the variable, it will show whatever number was last left in that part of the computers memory. At least in C++. A good compiler will warn you about using uninitialized variables, a source of many bugs. Sorry, this going off on a tangent a bit.

What about NAN?

Quote: JyBrd0403

Perhaps, it's better I directly ask the question. When you use the "number" 0, are you using a "number" to denote the absence of numbers (value, quantity)?

No, you're using a number to denote the absence of a quantity, not the absence of numbers. Numbers are not quantities. Numbers can sometimes represent quantities, but not always. It's hard to say you have -3 fish, and it's impossible to say you have 4i fish, but both -3 and 4i are numbers. You *can* say you have 0 fish, and 0 is also a number.

So the symbol 0 does not denote the absence of numbers, it denotes the absence of any amount of a thing, but it's the thing you're talking about, not a numeric abstraction. In order to denote "the absence of numbers" you can use set theory. The null set is a set with no numbers in it and that is denoted {}. The set of numbers with one number in it, specifically zero, is denoted {0}. There are lots of sets with no numbers in them, though. The set {Apple, Pear, Saxophone} is a set with no numbers in it, but three words. The cardinality of a set (the number of items in a set) is different from what that set contains. The cardinality of {} is 0.

Bottom line, the argument that 0 is not a number is analogous to the argument that "nothing" is not a word.

Quote: MathExtremist

No, you're using a number to denote the absence of a quantity, not the absence of numbers. Numbers are not quantities. Numbers can sometimes represent quantities, but not always. It's hard to say you have -3 fish, and it's impossible to say you have 4i fish, but both -3 and 4i are numbers. You *can* say you have 0 fish, and 0 is also a number.

So the symbol 0 does not denote the absence of numbers, it denotes the absence of any amount of a thing, but it's the thing you're talking about, not a numeric abstraction. In order to denote "the absence of numbers" you can use set theory. The null set is a set with no numbers in it and that is denoted {}. The set of numbers with one number in it, specifically zero, is denoted {0}. There are lots of sets with no numbers in them, though. The set {Apple, Pear, Saxophone} is a set with no numbers in it, but three words. The cardinality of a set (the number of items in a set) is different from what that set contains. The cardinality of {} is 0.

Bottom line, the argument that 0 is not a number is analogous to the argument that "nothing" is not a word.

This thread is a tale full of sound and fury, signifying zero.

num·ber
ˈnəmbər/Submit
noun
1.
an arithmetical value, expressed by a word, symbol, or figure, representing a PARTICULAR QUANTITY and used in counting and making calculations and for showing order in a series or for identification.



By definition a number is a PARTICULAR QUANTITY. -3 is a particular quantity, 4i represents a quantity(albeit an imaginary one). So, If you consider 0 a number, then you are using a particular quantity to denote the absence of any particular quantity. This is simply avoided by not considering 0 a number, quantity, value.

You can't just throw out the definition of numbers and then carry on. You can't say 0 is a quantity and then say it's not a quantity but it is a number. Can't do that by definition. On another thread someone just threw out the definition of the LLN and just carried on. If that's what this is, please don't bore me any further.

ze·ro
ˈzirō,ˈzēˌrō/
number
1. no quantity or number; naught; the figure 0


Zero by definition is no quantity or number. So, by definition it's not a number. You can't just throw out the definition of zero and say that there is no expression for a void of numbers, when that's what the definition of zero is. Can't just throw it out, and carry on.

So, by the definition of number, and zero, when you use 0, are you using a "number"(value, quantity) to denote the absence of numbers(value, quantity)?

You can still say yes I'm using a quantity to denote an absence of quantities, just like you can use an apple to denote an absence of apples. It just doesn't make any sense to do it like that, and would, by most people, be considered invalid.

Sigh. 0 is a number.
0 is an even integer.

https://en.m.wikipedia.org/wiki/0_(number)

Mathematics has clear definitions, axioms, and rules. It doesn't matter if they make sense to you.

If in your version of mathematics, zero is not a number, that's fine, but you won't be talking the same language as most other people.

Quote: Dalex64

Sigh. 0 is a number.
0 is an even integer.

https://en.m.wikipedia.org/wiki/0_(number)

Mathematics has clear definitions, axioms, and rules. It doesn't matter if they make sense to you.

If in your version of mathematics, zero is not a number, that's fine, but you won't be talking the same language as most other people.

In your version of math, 0 is a number, which is a particular quantity, and 0 is also the absence of a particular quantity, correct? So, 0 is a quantity representing no quantity? Is that correct? Can you see how that doesn't make sense?

Saying 0 is a number, is just making a statement, not defining the symbol.

Yes, in my version of math, 0 is a number. That is a statement which is true, because of the mathematical definition of zero.

Someone else defined it, though, not me. It does make sense to me, too.

If you really want to try bending your mind around something, look up aleph-null, omega, and how to count past infinity.

https://m.youtube.com/watch?v=SrU9YDoXE88

That guy has several videos on the topic.

Zero (0) is a NUMERAL, as well as a NUMBER. It is a symbol or name that signifies the absence of countable items.

It is nonsense to claim that zero is a "number that signifies the absence of numbers." Do we also claim that "NOTHING" is a word that signifies the absence of words and that "NOTHING" is therefore some kind of cosmic paradox? No way, Jose.

Quote: Dalex64

Yes, in my version of math, 0 is a number. That is a statement which is true, because of the mathematical definition of zero.

Let me ask you this. What is the definition of non-numeric. If zero is considered a number, is it also considered non-numeric? Once again, if 0 is simply not considered a number, then it easily converts to non-numeric.

Why can't we just use the webster's definition of zero.? It seems to be more accurate. Why are you allowed to just throw that out?

You mean this definition of zero?

http://www.merriam-webster.com/dictionary/zero

The one where it refers to zero as "the number zero" and "the number between the set of all positive numbers and the set of all negative numbers"?

Quote: Joeshlabotnik

This thread is a tale full of sound and fury, signifying zero.

That reference is the subtitle of the literature section at DT.

Quote: Dalex64

You mean this definition of zero?

http://www.merriam-webster.com/dictionary/zero

The one where it refers to zero as "the number zero" and "the number between the set of all positive numbers and the set of all negative numbers"?

Jeez, I walked right into that one, didn't I. LOL

Let me try it this way.

Would the below be an acceptable definition of "zero", is the verbiage acceptable?

- the arithmetical symbol 0 or 0̸ denoting the absence of all magnitude or quantity.

If the definition is acceptable, then I would say zero does not qualify to be a number. Which to me makes perfect sense. And, also would allow 0 to convert to non-numeric.

If you don't accept the definition of zero, the verbiage here, then do you have another definition? How about a definition for non-numeric?

Quote: JyBrd0403

In your version of math, 0 is a number, which is a particular quantity, and 0 is also the absence of a particular quantity, correct? So, 0 is a quantity representing no quantity? Is that correct? Can you see how that doesn't make sense?

No, it all makes perfect sense. Zero is the number that quantifies having none of something. But even numbers that can't quantify anything -- like i -- are still numbers.

If I ask you "what is the number of legs on a snake," are you actually bewildered by the question or do you understand that the answer is zero?

Quote: JyBrd0403

Jeez, I walked right into that one, didn't I. LOL

Let me try it this way.

Would the below be an acceptable definition of "zero", is the verbiage acceptable?

- the arithmetical symbol 0 or 0̸ denoting the absence of all magnitude or quantity.

If the definition is acceptable, then I would say zero does not qualify to be a number. Which to me makes perfect sense. And, also would allow 0 to convert to non-numeric.

Well, Mathworld has a similar definition but reaches an entirely opposite conclusion:

Quote: Mathworld entry for zero

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is neither negative nor positive. A number which is not zero is said to be nonzero. A root of a function f is also sometimes known as "a zero of f."

The first four words tell you that zero is a number.
http://mathworld.wolfram.com/Zero.html

The problem with your definition is that it is far too narrow. The symbol 0 represents a lot more than just "the absence of all magnitude or quantity" -- but not all uses of the symbol 0 represent the concept "zero" and vice-versa. Maybe that's where some of your confusion lies.

Just wanted to make one last point on the subject. In the youtube video (in the OP) the guy says 0 will follow "every" definition of an even number. That's why it's considered an even number.

What I'm pointing out is that it doesn't follow the MAIN definition of an even number. That is that an even number (as with all numbers) has a VALUE or QUANTITY. 0 doesn't fit that description, so it doesn't follow "every" definition of an even number. It may divide by 2 and all that, but it has no quantity or value, all other even numbers DO.

So, if you want to call it an even number, you would have to make an exception for 0 from all the other even numbers.

So, you would have to say something like 0 is an even number, with the exception that zero has no quantity or value, while all other numbers have quantity or value.

Which I quickly translate to .......... 0 is an even number, with the exception that it's not even a number.

Just make sure you notify people of that exception, when you explain to them that 0 is an even number.

That's all I'm sayin'.