Holey smoke! If you guys weren't well known, well educated, and well intentioned, I'd think all your squirrels had climbed way too high in the mathematics tree. I'd be happy to tell you that zero has always worked as an even number for me, but I still haven't figured out whether the square root of negative one is even or odd.

 

Oh, that's easy. The square root of an even number is even and that of an odd number is odd.
Hence the square root of -1 is also odd.

And I am 50% certain that I am wrong.

 

The only "odd" thing about the "even" number zero is ...

- you can multiply it by any number and get zero.
-you can divide it by any number and get zero.
-you can't divide it by itself to get any number because you can't divide by zero.

add that to the list we've seen above

 

...
-you can't divide it by itself to get any number because you can't divide by zero....

Isn't zero divided by zero = 1? You can get that answer using limits...

 

Isn't zero divided by zero = 1? You can get that answer using limits...

Which limit would that be? x^2/x or x/x^2?

 

You may find this interesting.

 

Isn't zero divided by zero = 1? You can get that answer using limits...

Zero divided by zero is undefined. I forget the proof, but that takes precedence over X/X = 1.

EDIT: Here's an explanation of why X/0 = infinity:

0/0 is undefined, but X/0 where X =/= 0 is infinity.

 

It has been said, but 0 is a special case. By most definitions though it is also even. I tend to look at a number line for my proof.

 

Isn't zero divided by zero = 1? You can get that answer using limits...

0/0 is a NaN:

http://en.wikipedia.org/wiki/NaN

 

It should also be noted that amilton's original question was about odd v even which strictly only applies to the Natural Numbers and the Integers, but not the Real Numbers. Positive and negative applies to the Real Numbers, but not the Complex Numbers.

 

For most practical matters the coast of England has infinite length, you'd be quite busy traversing it and measuring it on a millimetres scale, effectively, you wouldn't be able to do it actually.

Then you repeat it just on 1/10 mm scale, and probably, its shape has changed in the meanwhile.

sure, x + a = x is true, but parts of an equation that are equal to zero can be removed, so it doesnt make much sense.

As for the decimal system, it is just an agreement, that leftmost digits count 10x, 100x and so forth.
It is self contained kind of. You take the digit for one, shift it by one position, and substitute that for a number digit that doesnt exist such as "T" (for ten). In Hexadecimal that's "A" by agreement. The zero just says, the count for one-digits is none (but you can add some later).

Indeed you could store a number in a different format: Digit value and shift value, so ten would be 1.1
Its not very practical to do that you'd have to do it for each multiple of ten.

Zero isnt a number, just a technical means used to represent numbers, and also a means to express "nothing", or the "origin". It has special functions, and is a special case.

Arithmetic operations are either: Not defined, result in no change, or result again in zero.

As such, zero is "odd", even if as for integers you'd expect zero is even. I really dont think it's a number.

Using for instance 100 is just a way of expressing shifted digits, all added together, means 1*(10*10) + 0 *(10) + 0 * (1). If you are not comfortable with the fact the number "ten" contains a zero, simply imagine it as "9+1", because effectively that's what it is.

So the agreement is there are only 9 numbers, if the number is larger, it starts with 1 again, a zero is inserted, and the shifted 1 is counted as multiplicator for (9+1).

No wonder maths are so difficult and take years to learn in school.

The zero is just an indicator the number has been increased and was shifted, and the previous digit yet is zero.

 

For the benefit of those who read this thread but are unsure of the provenance of post#31, here are some corrections.

Arithmetic operations are either: Not defined, result in no change, or result again in zero.

False, for instance 0! is defined equal to 1

So the agreement is there are only 9 numbers

False, you have omitted an uncountable number of surds and transcendental numbers.

sure, x + a = x is true, but parts of an equation that are equal to zero can be removed, so it doesnt make much sense.

Zero isnt a number

How can something be equal to zero if zero is not a number?
It is your statement that makes no sense.

Further you should beware of 'removing zeros' from an equation. sometimes you can and sometimes you can't.

One interesting thing about zero is that it actually has two distinct meanings in mathematics, however you need some basic set theory to understand this.
With that under your belt it is a most fascinating exercise to go through the construction of all numbers from literally nothing at all.

 

Interestingly, when talking about nothing, something that isnt actually there at all, one can write quite a lot describing the odd circumstances accompanying the real-world dealings that inevitably occur from that.

When you put up a graphical "my world" representation from "your world", one could assume:

compatiblity = 0.0001

basically neglibly small for all purposes.

Sure you draw a special case of binary arithmetics, to proove yourself right.

There are only 9 numbers however. The number ten is again represented with "one", and a zero, showing it was shifted left by one decade.

Sure there are infinite numbers but they are all represented with only 9 different literals, and, you may guess that already, zero.

 

Most programming problems, difficulties and errors actually arise from the fact the true nature of zero isnt well understood. Once you understand its nature, and its multiple functions, you can deal with it:

Representing there is nothing, a position is start/origin.
Indicating the literal has cycled from 9 to 1 and it was shifted by a decade.

One time I have listened a long lamentation about Null pointers (back some while ago and now), and what is actually "null" from a Microsoft guy. Maybe I dont know properly what is null but he did.

If you consider null as a number, you will encounter programming problems.

 

Sure there are infinite numbers but they are all represented with only 9 different literals, and, you may guess that already, zero.

This is still false, repetition does not make it true.

Look up the definition of surds and transcendental numbers.

Pi would be a very well known counterexample to your claim.

 

... it is a most fascinating exercise to go through the construction of all numbers from literally nothing at all.

It's sort of like learning to play the Peano.

 

This is still false, repetition does not make it true.

Look up the definition of surds and transcendental numbers.

Pi would be a very well known counterexample to your claim.

When you describe what you are doing with your hand and how many fingers you use, and that involves zero fingers, you dont claim you are doing something with your hand. It just makes no sense.

Otherwise, using only one digit, there are numbers 1 to 9.
Then you use the next decade, starting again with 1.
The 1s then contain a zero as a placeholder.

And for fractional numbers its the same, just divide by 10 and shift right.

I dont understand the correlation surds- multiplying/dividing by ten- and expressing there is nothing.

When you write software you have to understand zero as what it really is or you will find it difficult to write programs.

If zero would be a number:

-Division by it would be defined
-Multiplication would yield a different result than again zero
-Addition and Subtraction would have an effect

Why do you insist its a number when for most aspects, it doesnt behave like a number?

If it really would be a number you would have to extend all numbers with an infinite amount of zeros on both sides of the decimal point. Since zero means there is nothing, you dont need to do this.

Numbers as we know it are just an abbreviation for instance 1234:

1x 1000 +
2x 100 +
3x 10 +
4x 1

Just because you have been indoctrinated with something at young age, dont neccessarily treat it as normal or even true or lets say "the way things are".

The consideration if zero is a number is as useful as to think about how a large piece of matter behaves when compressed into an infinitesimal small space (a black hole). There are countless elaborations about it.

Is infinitesimal small equal to zero? Or just almost zero for all practical matters?

Sure, not the same as a digital state of one or zero.

If the space is infinitesimal small still something is supposed to be contained, something is supposed to happen. what if it is actually zero? What's the point considering it, when it doesnt exist at all?

Maybe as absurd as these two parallel lines extending infinitely- they never meet and they dont exist as well- or probably they would as there is no exact positioning possible without a small abberation.

 

I dont understand

Exactly.

And until you respond to the things I have said, not to ones I didn't, I'm sorry to tell you that you are unlikely to.

For instance I didn't mention the binary system, computer programming, black holes or my fingers.

The is the Maths section and I have kept my comments to mathematical concepts about numbers.
Such concepts are obviously of great importance in maths and Man has spent at least 5000 years developing them.

And yes, that can make some aspects hard in school.

More information is there about what I did say if you want it.

 

Zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. The simplest way to prove that zero is even is to check that it fits the definition of "even": it is an integer multiple of 2, specifically 0 × 2.

 

I've always pondered this question when it came to Fourier series and I think I've just proved it.

Let any even number be equal to 2k for all k in Z, then if k=0, 2k=0, an even number. Just what was to be shown.

So... if k = 11 and 2k = 22, an even number, proves that 11 is an even number?

2k is an even number for ANY integer k, even, odd, or zero.