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# Mathematical breakthrough: Zero defined!

ocalhoun
For your mathematics-teacher-annoying pleasure I will now define zero as an even number. (as opposed to the old rule of "0 is neither even nor odd")
 Code: //This algorithim determines weather a number is even or odd input number if number / 2 is an integer    then output number+" is even"    else output number+" is odd" end if

Now, suppose we input 0 into this simple algorithim.
The result: 0 is even
this is because 0 is an integer, and 0 divided by any number is 0.

Now you might say that this algorithim cannot accurately check weather a number is even or odd, but it does work correctly for every number you can try.[/code]
Sappho
U dont need such an algorithm for it lets just take these rules which we have:

even+even = even
even+odd = odd

0+2 = 2 ( its even )
0+1 = 1 ( its odd )

Pretty much self-explanatory So 0 is even.
ml
0 is neither even or odd.

even ar numbers, tat have the factor 2 with a power of at least 0 in thier prime factor decomposition.

example: 28 = 2 * 14 = 2² * 7

you see, there is a two in there, so this number is even.

but 0 hasnt a prime factor decomposition, because 0 isnt a prime

=> you cant define, whether its even or odd
drunkfun
chuck norris / 0 is equal to a roundhouse kick to the face. NOBODY DIVIDES CHUCK BY ZERO!
raman
Very interesting, but nope.
NobodiesHero
I don't think 0 is a number. It stands for nothing, nix and nada.
So how can nothing be a number?

And if zero is not a number than it is neither even or odd.

quod erat demonstrandum
Soulfire
Zero is not defined, it is not a number. It is the lack, the absence of a number, hence 0. In your terms it may be defined, but in the textbooks and mathmaticians' minds, it isn't.
Nameless
How, exactly, is zero not a number? It is just as much of a number as 5 or -5. If anything, MORE of a number than -5 because it can be expressed in 'real' terms (eg, you can say someone has 0 apples, but not -5 apples).
Liu
 Nameless wrote: How, exactly, is zero not a number? It is just as much of a number as 5 or -5. If anything, MORE of a number than -5 because it can be expressed in 'real' terms (eg, you can say someone has 0 apples, but not -5 apples).

It's absense of a value.

Oh, and in terms of dividing by 0 since the other topic was locked, refer to people smarter than you:
http://mathforum.org/dr.math/faq/faq.divideby0.html

I'm not sure if you were trying to implement look-a-like code, but

number / 2 will always yield a true value, hence, every number that you input which is greater than 3 will say it's an even number.

Alternative code:

 Code: if (number % 2 == 0)   cout<<"num is even"; else   cout<<"num is odd";

edit: wrong on my part:
----------
Further, by this logic, it still doesn't make sense, because I can have:

 Code: if(number % 3 == 0)   cout<<"num is odd"; else   cout<<"num is even";

0 mod 3 = 0.

This makes it odd. However, 0 can't be odd or even at the same time, thus reductio absurdum.
-----------
avk
See girls are usually wrong
 Sappho wrote: U dont need such an algorithm for it lets just take these rules which we have: even+even = even even+odd = odd 0+2 = 2 ( its even ) 0+1 = 1 ( its odd ) Pretty much self-explanatory :) So 0 is even.

See u missed something...

It is that
odd+odd=====odd;
So,
0+1=1( its odd)
0+5=5( its odd)

so, Finally 0 is both odd and even .
nam_siddharth
Liu wrote:

 Code: if(number % 3 == 0)   cout<<"num is odd"; else   cout<<"num is even";

From where you got this stupid formula?
 Code: 7 % 3 != 0

Do you mean 7 is even?
nam_siddharth
avk wrote:
See girls are usually wrong
 Sappho wrote: U dont need such an algorithm for it lets just take these rules which we have: even+even = even even+odd = odd 0+2 = 2 ( its even ) 0+1 = 1 ( its odd ) Pretty much self-explanatory So 0 is even.

See u missed something...

It is that
odd+odd=====odd;
So,
0+1=1( its odd)
0+5=5( its odd)

so, Finally 0 is both odd and even .

From where you got this idea?

odd+odd=even without any exeption.
3+3=6
Do you mean, 6 is odd?
Sappho
avk wrote:
See girls are usually wrong
 Sappho wrote: U dont need such an algorithm for it lets just take these rules which we have: even+even = even even+odd = odd 0+2 = 2 ( its even ) 0+1 = 1 ( its odd ) Pretty much self-explanatory So 0 is even.

See u missed something...

It is that
odd+odd=====odd;
So,
0+1=1( its odd)
0+5=5( its odd)

so, Finally 0 is both odd and even .

Since when is odd+odd = odd? The rule is odd+odd = even
as:

1+1 = 2
3+7 = 10
17+31 = 48
.
.
.
Sappho
Liu wrote:

 Code: if(number % 3 == 0)   cout<<"num is odd"; else   cout<<"num is even";

0 mod 3 = 0.

This makes it odd. However, 0 can't be odd or even at the same time, thus reductio absurdum.

Try again?

It seems u arent too much of a mathematician, since when mod 3 makes numbers odd?

U mean like 6 mod 3 = 0 so 6 is odd?

Rofl
nam_siddharth
 Sappho wrote: Yes i am a girl, but that doesnt mean i am not right. Not talking about feminism, i am talking about the grey matter.

What is that gray matter?
Sappho
nam_siddharth wrote:
 Sappho wrote: Yes i am a girl, but that doesnt mean i am not right. Not talking about feminism, i am talking about the grey matter.

What is that gray matter?

U know the little thing called the brain
saiyeek
 Sappho wrote: U dont need such an algorithm for it lets just take these rules which we have: even+even = even even+odd = odd 0+2 = 2 ( its even ) 0+1 = 1 ( its odd ) Pretty much self-explanatory So 0 is even.

I loved it!
Liu
Ah, forgive me, long day at the lab; ignore mod 3.
bdoneck
an even number is defined as any integer times 2 so,
 Code: Even numbers = N * 2 ; where N is an integer Odd numbers = N * 2 + 1 ; where N is an integer

and plus, mathematicians who are way smarter than you have already defined zero as niether odd nor even, so this babbling about 0 is pointless
Sappho
 Liu wrote: Ah, forgive me, long day at the lab; ignore mod 3.

No problem, this is more of a fun topic than serious issue

 bdoneck wrote: and plus, mathematicians who are way smarter than you have already defined zero as niether odd nor even, so this babbling about 0 is pointless

Dunno about ocalhoun but i took this topic as fun and pointed out that there would be easier way to "prove" 0 as even number than his. Of course 0 isnt even nor odd couse 0 has no prime factor decomposition.
Garg
 NobodiesHero wrote: I don't think 0 is a number. It stands for nothing, nix and nada. So how can nothing be a number?

Yes but 0.000000000000000000000000000000000000000000000000001 is a number !! But it still is nada to most people !!!

Anyway, it depends how an even or odd number is mathematically defined... Just check any math book and apply the definition...

It's like a fruit is a eatible part of a plant that grows above the groung => a tomato is a fruit !
manumiglani
 Quote: Is Zero Even? Date: 03/28/2001 at 02:59:56 From: John Matousek Subject: Zero odd/even At numerous sites across the Internet the answer to the question whether zero is odd or even seems to be totally subjective, and the proofs used to justify 'even' (zero can be divided by two, therefore it is even), sound reasonable. But zero can't really be divided by two since the result is zero - neither a positive or negative integer. Q: How many times does 2 go into 0? A: Zero times. Or to rephrase, two doesn't go into zero. The question arose when a retired math teacher stated "2/20/2000, the first day ever with seven even numerals in its date." Of course he is wrong, 2/20/2000 BC being the most obvious example - if you accept zero as even. But there are also thousands of dates from the astronomical, Hebrew, Chinese, Hindu lunar, old Hindu solar and lunar calendars where zero would not even need to be considered. 'Ever' is such a big word. Thanks. Are these numbers odd or even? Date: 27 Apr 1995 12:18:53 -0400 From: Anonymous Subject: even or odd Hi, Would 2.5 be an even number, odd number, neither or both? Also, what about zero's evenness and/or oddness. Infinity's? Remember, time flies like an arrow, but fruit flies like a banana. Date: 27 Apr 1995 12:50:33 -0400 From: Dr. Ken Subject: Re: even or odd Hello there! The concept of even and odd seems to be one of the few cases in math where the intuition you learned in grade school will really hold true. Evenness and oddness only applies to the integers. So we don't discuss whether 2.5 is even or odd; it's like asking which American state the Atlantic Ocean is in, it just doesn't apply. It's neither. Zero, on the other hand, is very even. It can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Note that this lets you talk about whether negative numbers are even and odd. -7 is odd, and -8 is even. And since Infinity isn't an integer, it's also neither even nor odd. Thanks for the question!
nam_siddharth
Sappho wrote:
nam_siddharth wrote:
 Sappho wrote: Yes i am a girl, but that doesnt mean i am not right. Not talking about feminism, i am talking about the grey matter.

What is that gray matter?

U know the little thing called the brain

Then you want to say that you have brain! nice!!
Davidgr1200
[quote]Zero is not defined, it is not a number[/quote]

In that case which is the number exactly halfway between -1 and +1?
the_mariska
bdoneck wrote:

 Code: Even numbers = N * 2 ; where N is an integer Odd numbers = N * 2 + 1 ; where N is an integer

0 is an integer number, isn't is? So by your definition it should be even as well. I guess this discussion is pointless, just like the discussion whether 0 is a natural number, cause mathematical terms are abstract and conventional...
edallica
the multiplication symmetries must also be taken into account.

even*even=even
odd*even=even
odd*odd=odd

and now zero is shown to be neither neither odd nor even.

i believe this is what someone ment before and typed the + operator by mistake. people should have realised. clearly an odd number plus an odd number gives an even number!
Sappho
 edallica wrote: even*even=even odd*even=even odd*odd=odd and now zero is shown to be neither neither odd nor even.

Unfortunately that shows 0 as even number again:

1. lets say 0 is even and go with the rules:
[even*even = even]
0 * 2 = 0 even - so that works
[odd*even = even]
3 * 0 = 0 even - that works too

SO IT WORKS WITH 0 AS EVEN NUMBER

2. lets say 0 is odd:
[odd*odd=odd]
0 * 0 = 0 odd - that works
[odd*even = even]
0 * 3 = 0 odd (should be even) - SEE HERE IT PROVES THAT 0 CANT BE ODD

So u can prove that 0 cant be Odd number with these rules but still can be even.

Anyway as i said it all depends on definition of even number, which is commonly defined as a number with prime number decomposition containing 2^x where x>0 and thats not true for 0 since 0 has no prime number decomposition )
earthchild
 avk wrote: See girls are usually wrong

nilsmo
Zero is even according to Wikipedia (http://en.wikipedia.org/wiki/Odd_number) and my second grade teacher... Zero is a mysterious integer though.

And, NobodiesHero, zero is mathematically considered a number (though it is not a counting number like 1,2,3,4,5,6...). Even imaginary numbers are numbers. Numbers are a unit of measurement. 0 measures something just like -3 does.
psycosquirrel
Zero is a number. Think of it this way:

4-2 = 2 (integer)
3-2 = 1 (integer)
2-2 = 0 (integer)
1-2 = -1 (integer)
0-2 = -2 (integer)

Also, functions must be defined all throughout their domain and range. Consider the line y = x. The functions domain and range are all reals, and therefore, it is continous through all values. Since the function passes through (0, 0), then 0 is a defined point on the graph, proving it as a value, and therefore, a number.
tidruG
Sorry boys and girls... "0" called. It no longer wants you to debate on whether it's odd or even... it's like debating whether a eunuch is a male or a female, whereas it is really both and neither.

In the end, what we can agree on is that 0 is a number, and one of the most important ones. If there was no number as 0, then I could say to someone "You owe me XX amount of money", where the XX would have some value, which is not "nada" or "nothing" or "zilch"... meaning you always owe me some value.
Daniel15
Speaking of 0, I was wondering about 0/0 (0 divided by 0) the other day. My friend was saying that if you divide any number by itself, you get 1 (eg. 7/7 = 1, 4/4 = 1, etc.). From that, he was saying that 0/0 must equal 1. Another friend was saying that 0 divided by any number must equal zero (eg. 0/7 = 0, 0/4 = 0). So, 0/0 must equal 1.

In fact, 0 divided by 0 can be any number! This is why people say that 0 divided by 0 is 'undefined'.

Take this simple example: Using Algebra, you can reorder a sum. For example, consider this:
y X 7 = 14 (y multiplied by 7 equals 14)
To find the value of 'y', you could reorder the sum, to make y the subject:
14 / 7 = y (14 divided by 7 equals y)

From that, you can obviously see that y equals 2. However, any number multiplied by 0 will always equal 0. So, consider this:
y X 0 = 0 (y multiplied by 0 equals 0)
Fair enough? What if you rearrange it:
0 / 0 = y (0 divided by 0 equals y)

That means that 0/0 = y. Therefore, 0 divided by 0 can equal anything!

 Quote: In the end, what we can agree on is that 0 is a number, and one of the most important ones

Agreed, 0 is one of the most important, if not THE most important number. One of the bad points of Roman Numberals was that they had no '0', so they had no way of saying 'Nothing'

EDIT: Fixed stupid mistake
nam_siddharth
 daniel15 wrote: Speaking of 0, I was wondering about 0/0 (0 divided by 0) the other day. My friend was saying that if you divide any number by itself, you get 1 (eg. 7/7 = 1, 4/4 = 1, etc.). From that, he was saying that 0/0 must equal 1. Another friend was saying that any number divided by 0 must equal zero (eg. 7/0 = 0, 4/0 = 0). So, 0/0 must equal 1.

how come 7/0=0?
7/0= infinite.
0/7=0
Daniel15
nam_siddharth wrote:
 daniel15 wrote: Speaking of 0, I was wondering about 0/0 (0 divided by 0) the other day. My friend was saying that if you divide any number by itself, you get 1 (eg. 7/7 = 1, 4/4 = 1, etc.). From that, he was saying that 0/0 must equal 1. Another friend was saying that any number divided by 0 must equal zero (eg. 7/0 = 0, 4/0 = 0). So, 0/0 must equal 1.

how come 7/0=0?
7/0= infinite.
0/7=0

It was meant to say that 0 divided by any number will equal 0. Fixed now
the_mariska
Aargh.. Haven't you heard that dividing by 0 is forbidden? This goes from the definition of division, where:
a/b = c means that a = b * c.

If we assume that b = 0, we get:
0 * c = 0, no matter what are the numbers a or c.

There should be one exception, 0/0, and this would be 0, cause 0 * 0 = 0, but I'm not quite sure if this is allowed, too.

Is there still anyone who considers 0 as a no-number? Numbers are not only the natural numbers (1, 2, 3, 4 ..) and not even real (eg. -1/2, 2 3/4) but there are also purely imaginatory numbers like the square root of -1. This all isn't as easy as it seems
Sappho
 the_mariska wrote: Aargh.. Haven't you heard that dividing by 0 is forbidden?

Yes but its forbidden couse the result is infinity as 7/0 is infinity but for infinity even if its a number (thou imaginational) no associative rules apply. Its impossible to work with such a number so its better solution to forbid x/0 than make up extra rules.

But i bet there is no universal definition that is accepted by all mathematicians. Its rather pointless to discuss it further.
benjamincblunt
Hey everyone. I just wanted to say that I hate to do this but it has been scientifically proven by a student in Denver, Colorado that zero equals one. Feel free to put any input you may have about this but no one has been able to prove this guy wrong yet and her used straight up proofs and theroms to define his answer and not one step has been proven wrong yet. Tell me what you think about this.
novisdesign
Thats one of the dumbest things i've ever herd. 0 is a great number tho, i love it.

peace

THIS JUST IN 1+1=3
the_mariska
 Sappho wrote: Yes but its forbidden couse the result is infinity as 7/0 is infinity but for infinity even if its a number (thou imaginational) no associative rules apply. Its impossible to work with such a number so its better solution to forbid x/0 than make up extra rules.

Not exactly. If we divide 7 by very little but positive numbers (eg. 0,0000001) and each one is less than the previous one, each of the results will be nearer to infinity. But if you take negative numbers, that are almost 0, the results will be nearer to negative infinity (we write this lim n-> 0+ (7/n) = inf. ; lim n-> 0- (7/n) = -inf.) So you can't just say that x/0 is infinity, cause this can be - infinity as well
 Quote: There should be one exception, 0/0, and this would be 0, cause 0 * 0 = 0, but I'm not quite sure if this is allowed, too.

Forget bout this, I don't know why I wrote such a BS. Maybe because I hadn't slept the night before at all
 Quote: Hey everyone. I just wanted to say that I hate to do this but it has been scientifically proven by a student in Denver, Colorado that zero equals one. Feel free to put any input you may have about this but no one has been able to prove this guy wrong yet and her used straight up proofs and theroms to define his answer and not one step has been proven wrong yet. Tell me what you think about this.

Well, if I saw his 'proof' I'd search for a mistake, but without it the discussion is pointless. And I can proof that (1 - 1/2) equals (1 + 1/2) and not many people discovered what was wrong about it
Sappho
the_mariska wrote:
 Sappho wrote: Yes but its forbidden couse the result is infinity as 7/0 is infinity but for infinity even if its a number (thou imaginational) no associative rules apply. Its impossible to work with such a number so its better solution to forbid x/0 than make up extra rules.

Not exactly. If we divide 7 by very little but positive numbers (eg. 0,0000001) and each one is less than the previous one, each of the results will be nearer to infinity. But if you take negative numbers, that are almost 0, the results will be nearer to negative infinity (we write this lim n-> 0+ (7/n) = inf. ; lim n-> 0- (7/n) = -inf.) So you can't just say that x/0 is infinity, cause this can be - infinity as well

tidruG
 the_mariska wrote: Aargh.. Haven't you heard that dividing by 0 is forbidden?

Well, it's not exactly forbidden. Anything divided by 0 is infinity, which is basically undefined and cannot be worked with in practical/theoretical cases. This is why dividing by zero is avoided, but not exactly forbidden.

 Sappho wrote: But i bet there is no universal definition that is accepted by all mathematicians. Its rather pointless to discuss it further.

Yeah I agree.

 benjamincblunt wrote: Hey everyone. I just wanted to say that I hate to do this but it has been scientifically proven by a student in Denver, Colorado that zero equals one. Feel free to put any input you may have about this but no one has been able to prove this guy wrong yet and her used straight up proofs and theroms to define his answer and not one step has been proven wrong yet. Tell me what you think about this.
Probably some sort of a hoax... I'll believe it when I see the proof. Until then, I'll stick with my common sense... because if 0=1, then you owe me (1,000,000 * 0) USD... you decide what 0 is there...

 the_mariska wrote: So you can't just say that x/0 is infinity, cause this can be - infinity as well

Excellent point. I was waiting for someone to bring this up... this is the reason why x/0 is not considered infinity, but undefined.
toughtrio
This is just done by an algorithm. It doesnot prove, in any ways, that 0 is an even number.

Warm Regards,
z3nm4n
Did you all know that the earliest inventors of the number '0', pythagoras and his followers, had a rule that anybody that would disclose the nature of their discovery to the outside world would be put to death immediately. 0 was the centerpiece of their filosophy and considered extremely dangerous in it's implications...

I can confirm that. Since we started to use the *peep* thing it keeps popping up on my account slips
chargoyle
Like it's already been pointed out, zero isn't a number that plays well with all the others. Zero has too many oddities about it in mulitplication, division and graphing that, to mathematicians, it's not a normal even or odd number. But one thing to think about is the fact that you cannot divide zero, supposedly. But that begs the question if zero even IS a number, since any number divided by itself is 1. Zero divided by zero is undefined or zero, according to textbooks. So is zero divided by itself, zero, one, infinity, or some other number that we need a greek letter for?
Soulfire
Well actually, 7/0 = undefined. Why is that? Oh... it's because 0 is undefined.
Nyizsa
So, division by zero is undefined. Yes, but as someone has mentioned, we have the limes to get an idea what happens if we have to divide by a number very close to 0. We have the tools to make this defined.
Again, 0 shows the charasteristics of both odd and even numbers. It is convenient to consider it as an even number. (Think of ...-2, -1, 0, 1, 2...)
 the_mariska wrote: And I can proof that (1 - 1/2) equals (1 + 1/2) and not many people discovered what was wrong about it

Sounds interesting! Could you send it to me in a private message? Just for fun...
SunburnedCactus
I'm surprised no-one has slipped in the square root of -1 yet, or a crazy complex number like 2 + 3j. That would certainly weird things out a bit.
tidruG
 SunburnedCactus wrote: I'm surprised no-one has slipped in the square root of -1 yet, or a crazy complex number like 2 + 3j. That would certainly weird things out a bit.

Primarily because 0 has nothing much to do with complex numbers...
And it's complicated enough without having anything to do with them, so let's not inject unrequired ideas into peoples' heads
nam_siddharth
 benjamincblunt wrote: Hey everyone. I just wanted to say that I hate to do this but it has been scientifically proven by a student in Denver, Colorado that zero equals one. Feel free to put any input you may have about this but no one has been able to prove this guy wrong yet and her used straight up proofs and theroms to define his answer and not one step has been proven wrong yet. Tell me what you think about this.

do not prove now that black=white
SunburnedCactus
tidruG wrote:
 SunburnedCactus wrote: I'm surprised no-one has slipped in the square root of -1 yet, or a crazy complex number like 2 + 3j. That would certainly weird things out a bit.

Primarily because 0 has nothing much to do with complex numbers...
And it's complicated enough without having anything to do with them, so let's not inject unrequired ideas into peoples' heads

Well frankly with some of the ideas here it seems that a few people have had that injection already.
Ultima1080
Here's what I think the original guy that started this topic did. You defined the COUNTING NUMBER zero...not the actual absense of a number. In the computer's eyes (or whatever analogy you want to use) 0 is just another number. However, zero is meant to mean the lacking of any value. So you determined that the "place holder zero" is even. I think anyone could have told you that, especially considering that numbers alternate even and odd throughout the numerical system. So, actually zero is still the absense of anything. As for the square root of -1...no, just stop. You can't take the square root of a negative number, because no number squared will EVER give you a negative number. Unless you try to pull some bullshit with "i". In which case...you'd still be wrong.
Sappho
 Ultima1080 wrote: As for the square root of -1...no, just stop. You can't take the square root of a negative number, because no number squared will EVER give you a negative number. Unless you try to pull some bullshit with "i". In which case...you'd still be wrong.

U dont need to pull some bullshit with i as u said it, couse actually i is defined as square root of -1. Actually i and -i are both the result of square root of -1
[FuN]goku
i dont think anyone knows what 0 is tbh, there are books and books written
on the number 0, according to my math/science teacher actually maybe 0 is like infinity or sumthing,,
webapp
it is a quite interesting..............

 psycosquirrel wrote: Zero is a number. Think of it this way: 4-2 = 2 (integer) 3-2 = 1 (integer) 2-2 = 0 (integer) 1-2 = -1 (integer) 0-2 = -2 (integer) Also, functions must be defined all throughout their domain and range. Consider the line y = x. The functions domain and range are all reals, and therefore, it is continous through all values. Since the function passes through (0, 0), then 0 is a defined point on the graph, proving it as a value, and therefore, a number.
Nyizsa
 benjamincblunt wrote: Hey everyone. I just wanted to say that I hate to do this but it has been scientifically proven by a student in Denver, Colorado that zero equals one. Feel free to put any input you may have about this but no one has been able to prove this guy wrong yet and her used straight up proofs and theroms to define his answer and not one step has been proven wrong yet. Tell me what you think about this.

Well, I wonder what kind of computer this guy is using... with one symbol only?
the_mariska
 [FuN]goku wrote: i dont think anyone knows what 0 is tbh, there are books and books written on the number 0, according to my math/science teacher actually maybe 0 is like infinity or sumthing,,
I don't get your point, how can 0 be something like infinity ? I'm not a philosopher, I have rather a scientific mind so for me 0 is just 0, nothing more. :]
 Quote: As for the square root of -1...no, just stop. You can't take the square root of a negative number, because no number squared will EVER give you a negative number. Unless you try to pull some bullshit with "i". In which case...you'd still be wrong.

Why do you think so? I've heard it somewhere: "God created the natural numbers, all the rest was invented by people." We'd better not discuss if God created numbers or not, the point is that in maths there can be numbers that have no examples in reality, the only limits are the limits of your mind. (BTW. I've heard that some scientist hypothetically assumed that there are some molecules which mass is i units, that move backwards in the time, and later he proved that they exist . So you can see that i is not a complete absurd )
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