The Instigator
Rockylightning
Pro (for)
Losing
0 Points
The Contender
Chrysippus
Con (against)
Winning
11 Points

Zero is an even, not odd, number.

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Post Voting Period
The voting period for this debate has ended.
after 3 votes the winner is...
Chrysippus
Voting Style: Open Point System: 7 Point
Started: 11/9/2011 Category: Education
Updated: 5 years ago Status: Post Voting Period
Viewed: 7,468 times Debate No: 19212
Debate Rounds (4)
Comments (17)
Votes (3)

 

Rockylightning

Pro

First round is for acceptance.
My opponent must prove that zero is not an even, but an odd number.
I will begin my arguments at the beginning of round 2.
Chrysippus

Con

I accept.
Debate Round No. 1
Rockylightning

Pro

I thank my opponent for accepting this debate. Let's get started!

I will go about arguing by first reviewing what defines an even number, then comparing these attributes to the attributes of zero.

WHAT IS AN EVEN NUMBER?
Good Question!
An even number is most obviously divisible by two, but it shares many other unique properties.

Let's prove what an even number is using the three smallest even numbers: 2,4, and 6.

Let's start with the simplest and easiset to understand way of defining an even number.
1. An even number plus an even number equals an even number.
2+4=8
An Even number plus an odd number equals an odd number.
2+3=5
An odd number plus an odd number equals an even number.
3+3=6


2. An even number is between two odd numbers on a number line.
2 is surrounded by 1, and 3. 1,2,3.

3. An even or odd integer multiplied by by an even number equals an even number.
2x4=8
10x3=30

4. An odd number multiplied by an odd number, equals an odd number.
3x3=9
13x1=13
9x5=45

Now let's examine zero's properties.
Le'ts plug zero into these various equations. *Refer to the numbers put up above*
1. 0+4=4. 4 is even, ergo zero is even.
0+3=3. 3 is odd, ergo zero is even.
0+5=5. Five is odd, odd numbers added to eachother are even, ergo zero is even.

2. 0 is surrounded by 1, and -1. Both are odd, and only even numbers are surrounded by odd numbers, ergo zero is even.

3. 2x0=0. Nothing can be concluded however by this, because for this to be true, we must postulate that zero is even, though with the evidence above, zero is even.

4. 0x3=0. Again, postulating that zero is even, an odd number times an even number equals an even number.



I think that's enough for now. I can't wait to see what Chrysippus comes up with.
Chrysippus

Con

My thanks to Rockylightning for this debate.

I admit, I initially accepted this debate because the premise is slightly abusive. Debates that argue "1=1" and "My user name is Chrysippus" are usually put out for an easy win, and thus invite smart-alecs to come out of the woodwork and twist things around with a semantical argument. That, I admit, was my initial motivation.

This debate, though, admits a greater scope for argument than my first glance showed; and as long as I have Rockylighting's solemn word that he will not instant-win this debate by going to a certain online mathematics dictionary and pointing out that the definition of Zero classifies it as an even number, but instead will limit himself (as I will) to the pure exercise of logic within this debate, we can have fun. In which case, I will shelve the reams of potent arguments I have ready to prove that Zero is an odd (in the sense of "unusual") number.


Ready?




The burden I accept in this debate is to show that Zero is not an even number.




---------------I contend Zero is not an even number----------------



Pro stated several characteristics of even numbers; and I agree with all of them. All four points under "What is an even number?" but before "Now let's examine zero's properties" I readily concede to be essentially correct.

The disagreement starts when he begins to examine zero itself. I will use his numbering system to keep track of the items:

1. Instead of the normal rules of "even + even = even, odd + even = odd", it seems that zero has its own special rule: "Anything plus zero is itself." This holds true no matter what is added to zero, indicating we may be dealing with a special case.

2. Even numbers are certainly sandwiched between two odd numbers, and zero is in between 1 and -1; but notice that zero is the only number that is between integers of positive and negative value. No other even number (if zero were an even number) has this characteristic.

3. Anything times an even number IS a larger even number; but anything times zero is zero, not some larger even number. Again, zero breaks the rules for even numbers.

4. Here Pro makes a mistake in his writing; the rule he gave initially for 4 is "odd times odd = odd", not "even times even = even." And zero shows again that it is not bound to the rules for even numbers, because anything(odd or even) times zero = zero. Rules 3 and 4 show that zero is neither even nor odd, because operations using zero violate the rules for either category.




Now, he did mention one other very, very important rule for even numbers; but he glossed over it. Gentlemen, ladies, I present to you the noble 2.

All even numbers are evenly divisible by two; or, more cogently to this debate, are able to be expressed as multiples of two. 100 can be divided evenly into two 50's, and can be expressed as 100=(2*2*25).

Odd numbers cannot be divided evenly by two. 33 can be expressed as 33=(3*11), but is not expressed as (2*16.5). Odd numbers cannot be evenly divided by even numbers, and can only be evenly divided by numbers that are factorial to them.

Two itself cannot be divided by odd numbers without departing from the realm of whole numbers.



Ah, and one more thing.

Since even numbers all have the common factor of two, large even numbers can be divided evenly by many of the even numbers lower than it on the number line. 100 can be divided by fifty, twenty, ten, four, and two. 160 can be divided by eighty, forty, thirty-two, twenty, sixteen, ten, eight, four, and two. (They can both also be divided by five, but that does not concern us at the moment.)

This is all very obvious stuff, and I apologize to the kindly reader for dragging you through it; but it is all neccessary, I assure you.





Let us look at how zero treats 2.


Zero divided by two is zero. Zero divided by any number is zero. If zero were even, we would expect it to be evenly divisable by two, but not by every odd number as well.

Zero cannot be expressed as a multiple of two: {2=(0*?)}

Two cannot be divided by zero, of course; and neither can any other even number. No even number has zero as a factor. For that matter, no odd number does, either.



If no even number has zero as a factor; if zero always divides zero times, no matter whether divided by even or odd integers; if zero cannot be expressed as a multiple of two, unlike any even number; and if zero acts independently of all the even numbers when the 4 rules given by my opponent are applied; we can conclude:

Whatever zero is, it certainly isn't even.






I postulate that zero is a special case, neither even nor odd; but as it does not follow the rules for an even number, it is absurd to argue that it is even.


I return this debate to my opponent, and wish him the best of luck.

-C
Debate Round No. 2
Rockylightning

Pro

Here is the long awaited rebuttal.

"The burden I accept in this debate is to show that Zero is not an even number."
Agreed.

To make it easier to read my rebuttal, I will put quotes in Italics as well as in quotations, and my refutations in bold.


Rebuttal


1. "seems that zero has its own special rule: "Anything plus zero is itself." This holds true no matter what is added to zero, indicating we may be dealing with a special case."

While this is very unusual, we must examine 1. The properties of the numbers being put together, 2. The properties of the number that comes out. 3. The properties of zero.
Take this example: 2+0=2.
The number 2 is even. Zero is unknown.
The sum of the two is even.
Even though the sum of the two numbers is the first number, 2 and 2 share the same properties of eveness and therefore, according the the properties of even number addition, zero is even.

2. "notice that zero is the only number that is between integers of positive and negative value. No other even number (if zero were an even number) has this characteristic."

Every number has unique charictaristics. Please explain what importance the negative and positive values of its neighbors have. That's like saying that "thirteen is the only number that is sandwiched between 12 and 14, no other number has that charictaristic".

3. "Anything times an even number IS a larger even number; but anything times zero is zero, not some larger even number. Again, zero breaks the rules for even numbers."

Again, while zero is an anomaly, that does not negate that it is even.

4. "because anything(odd or even) times zero = zero."

If 2x0=0 and 3x0=0, then the products are the same. If even times even is even, and odd times odd is odd, then zero is definitely both even, and odd. But since zero is applicable to the properties stated above, it can be deduced that zero is even.




"Two cannot be divided by zero, of course; and neither can any other even number. No even number has zero as a factor. For that matter, no odd number does, either."


Exactly, zero is simply null for many properties of real, even numbers, though with the properties stated in my points 1 and 2, zero should be considered even.



Conclusion:

Every number, positive or negative, even or odd, real or imaginary, shares unique properties. Zero is an anomaly in many terms of numbers, but it shares many more charictaristics with even numbers than it does with odd numbers, and for these contentions, zero should be considered even.


Back to you Chryssipus.
Chrysippus

Con

I want to place this here, the first thing you will see when reading my argument:

Zero does not have two as a factor; it cannot be expressed as a multiple of two.

EVERY EVEN NUMBER DOES AND CAN.

It is the most basic element of even numbers, that every single one of them can be divided into two equal halves.

Zero, having no factors and no value, cannot be divided into two equal halves; it returns a null result, because there is nothing there to divide.

Zero cannot be an even number.


My opponent chose not to respond to this, or really to any of my arguments from the last section of my R2; but this is probably the most important part of my argument. I COULD say that by dropping this argument, my opponent has conceded the debate, but I would like to hear my opponent explain why zero should be the ONLY even number not expressible as a multiple of two; why the most basic rule of even numbers should be waived in zero's case.

You know, along with all the other rules for even numbers that we'd have to make special exceptions for to shoehorn zero in. LIke how anything times an even number is another (larger!) even number, but anything times zero is nothing. Or how zero seems to follow (and break) the rules for odd numbers with equal facility as those for even. Or how no even number has zero as a fraction, while every even number is a factor to some higher even number.



Now to deal with my opponent's case:

1. What you are missing here is that zero does not change anything you add to it. The rule that applies here is not "Even + even = even, odd + odd = even, odd + even = odd;" the cases for addition with zero has it's own rule: "Anything +zero is itself."

Even numbers add to even numbers to make larger even numbers. Odd numbers add to odd numbers and make larger even numbers. Odd numbers add to even numbers and make larger odd numbers.

But anything that you add zero to remains the same. It doesn't grow, it doesn't shrink, and if it could be divided by two before the operation it can still be so divided. Zero lacks value, which is a necessary property for these rules for even numbers.


2. Zero's position as the null point, the beginning of the number line, doesn't strike you as something special? You really don't see any difference between the reference point common to all number lines/axis and, say, the position of 345 between 344 and 346?

Your argument was "An even number is between two odd numbers on a number line." And yes, they do alternate. This happens to be the best argument you have for zero being even. If it weren't for the fact that zero's unusual position hints at it having unusual properties, and the fact that zero casually breaks all the other rules for even numbers, you might have a point here. Zero occupies a unique place as the null point; the first real number (1) logically has to be an odd number, but that does not necessarily make zero even. If anything, this position implies that zero is neither even nor odd.


3 and 4. You cannot just handwave this. Saying "that does not negate that it is even." without any reasoning or justification isn't an argument; it's just a bald statement of your opinion.

For this point and 4, you presume zero to be even. You effectively say, "Although zero does not fit the rules for even numbers here, that's ok; points one and two are enough, you can trust me when I tell you it's even."

I provided logical arguments showing how zero does not fit the rules here, and why it is important; for you to dismiss these as irrelevant anomalies is not a defense of your case.

You've effectively conceded these two points.




To recap:

Zero does not have two as a factor; it cannot be expressed as a multiple of two.
Every even number has two as a factor, and can be expressed as a multiple of two.
:. Zero is not an even number.

even + even = larger even
anything + 0 = itself.
:. Zero is not an even number.

Number alternate odd and even.
Zero occupies a unique place as the null point; the first real number (1) logically has to be an odd number, but that does not necessarily make zero even.

Anything times an even number is a larger even number.
Anything times zero is itself.
:. Zero is not an even number.

An odd number times an odd number is a larger odd number.
Anything times zero is itself.
:. Zero is not an odd number.

Conclusion is obvious.

I return the debate to my opponent.

-C
Debate Round No. 3
Rockylightning

Pro

Rockylightning forfeited this round.
Chrysippus

Con

I really have nothing further to add. Extend all my arguments; vote Con!



-C.
Debate Round No. 4
17 comments have been posted on this debate. Showing 1 through 10 records.
Posted by F-16_Fighting_Falcon 4 years ago
F-16_Fighting_Falcon
RockyLightning had it made but then for whatever odd reason threw away the debate in Round 3.

Round 1, he says, "My opponent must prove that zero is not an even, but an odd number."

Chryssipus accepts this and then changes the burden to "The burden I accept in this debate is to show that Zero is not an even number."

All RL had to do was reject it saying that that is not what Chrys agreed to and it would have been an auto-win. Instead, he literally throws this debate away with all his strength like baseball pitcher by accepting Chrys's statement about what his burden should be.
Posted by Rockylightning 5 years ago
Rockylightning
Darn. I lost track of time, I had too many exams on friday...
Posted by Chrysippus 5 years ago
Chrysippus
Good debate, Rocky. Thanks for letting me play.
Posted by Rockylightning 5 years ago
Rockylightning
*formulates thoughts*
Posted by Chrysippus 5 years ago
Chrysippus
*waits*
Posted by Chrysippus 5 years ago
Chrysippus
Says the guy sporting the picture of the airborne Welsh Corgi.
Posted by Rockylightning 5 years ago
Rockylightning
Deal. Though its hard to take you seriously with that avitar.
Posted by Chrysippus 5 years ago
Chrysippus
So. I won't twist the definition of "Odd" to win, and you can't define your way to victory either. Deal?

Besides, I think we've got the makings of a good debate here. Looking forward to seeing what you come up with.
Posted by Chrysippus 5 years ago
Chrysippus
Would I ever do such a thing?

I DID come up with several ways in which Zero is an unusual number, but since you asked nicely I'll play fairly.
Posted by Rockylightning 5 years ago
Rockylightning
Oh, and please don't make this a semantic bull poop debate. Mkay?
3 votes have been placed for this debate. Showing 1 through 3 records.
Vote Placed by Chuz-Life 5 years ago
Chuz-Life
RockylightningChrysippusTied
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Total points awarded:03 
Reasons for voting decision: I have only enough time for a short observation; It appears to me that "0" is a number in name only. Pro's persistence and attention to detail not withstanding, Con's rebuttals to those points (for me) solidified the evidence that "0" itself is neither odd nor even in any one particular equation. Nothing FROM nothing leaves nothing. Nothing PLUS nothing leaves nothing. And two "nothings" alone and apart one from the other is nothing.
Vote Placed by Kinesis 5 years ago
Kinesis
RockylightningChrysippusTied
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Reasons for voting decision: Fascinating debate - not for the conclusion, which it just a matter of definition as far as I can tell, but for the argumentative process used by both Pro and Con in the first round. Con showed that zero is sufficiently distinct from other even numbers to warrant considering it not even.
Vote Placed by imabench 5 years ago
imabench
RockylightningChrysippusTied
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Reasons for voting decision: Pro had a really good starting case but Con showed the unique qualities of Zero compared to all other numbers so he won arguments. Also pro forfeited the last round so that gives conduct to con. Pretty good debate, well done