Ask a Question
or
Create a Poll
  1. Home /
  2. Questions /
  3. Science
  4. / Mathematics
  5. / Zero

by BuckyF on October 16th, 2003

BuckyF

Question

Help answer this question below.

Is zero considered an even or odd number, or neither?

  • Like
  • Report
Share:
Other

Answers. 43 helpful answers below.

  • by worshiptool on March 23rd, 2007

    worshiptool

    Zero is an even number

    An even number is a number that
    is exactly divisible by 2. That means that when you divide by two the
    remainder is zero.

    • Like
    • Report

    2 comments | Post one | Permalink

  • by lunatik on December 7th, 2003

    lunatik

    This one makes me smile.

    Zero is an even number. All whole numbers and positive and negative integers are either ODD or EVEN.

    Just remeber the number line if you have any doubts.

    ... -3 -2 -1 0 1 2 3 ...

    Go back to the rules on odd and even. (3rd grade I think)

    O= odd and E= even

    E + E = E
    O + O = E
    O + E = O

    -2 + 2 = 0
    -1 + 1 = 0
    -1 + 2 = 1

    I hope this settles this.

    • Like
    • Report

    6 comments | Post one | Permalink

  • by BlondeMathGeek on February 4th, 2004

    BlondeMathGeek

    http://www.straightdope.com/mailbag/mzeroeven.html

    An even integer has no remainder when divided by 2. An odd integer can be written in the form 2N + 1 where N is some integer.

    The exclusion of zero from the even numbers does occur under special circumstances. If you are defining even numbers to mean even NATURAL numbers, not even INTEGERS. The natural numbers are the set of counting numbers {1, 2, 3, . . .} which excludes zero.

    There may be special other circumstances in which you want to deal with a set called "even" that excludes zero. For instance, Goldbach's conjecture (unproven, I think, to date) is that every even integer greater than 2 can be expressed as the sum of two primes. But that conjecture also excludes 2 from the selected set of "even integers" being considered.

    If you're at the roulette table, you bet "evens" and the ball lands on 0 or 00, you lose. So that's a non-mathematical, real-life situation where zero is neither odd nor even.

    • Like
    • Report

    1 comment | Post one | Permalink

  • by Christopher Woods on January 21st, 2004

    Christopher Woods

    Surely zero is only a representative figure for the absence of an amount, just like black and white are not colours in themselves, merely an absence of colour... In which case, zero is neither even nor odd, as it doesn't exist.


    Something to think about.

    • Like
    • Report

    3 comments | Post one | Permalink

  • by branciforte3241 on April 1st, 2007

    branciforte3241

    A cleaner definition of "even" is this: X is even if there exists another integer N such that 2 times N is equal to X. In algebraic terms this avoids the division operation that can get complicated when run negative numbers through our rings and modoules. Division works, but I find the multiplicative definition to be much more elegant.

    And, yeah, zero is even.

    • Like
    • Report

    2 comments | Post one | Permalink

  • by DeuceOfSpades on November 9th, 2003

    DeuceOfSpades

    It's neither. Both zero and 1 are what are known as composite numbers. And yes, 0 is divisable by 2. 0/2=0.

    EDIT: Ok. It's a faulty answer. Quit rating me several months after I posted this.

    • Like
    • Report

    3 comments | Post one | Permalink

  • by Cesar Alejandro on October 17th, 2003

    Cesar Alejandro

    Zero is not positive or negative... but it IS EVEN.
    http://mathforum.org/library/drmath/view/57188.html

    • Like
    • Report

    1 comment | Post one | Permalink

  • by FakePlasticTrees on October 16th, 2003

    FakePlasticTrees

    Not sure on the actual answer, but I would have to say it is even by this reasoning:
    Even numbers are in the form 2n
    Odd numbers are in the form 2n - 1
    So, by plugging in numbers into n, you get either even or odd numbers depending on which formula you used. So for example:
    Even: 2(1) = 2
    Odd: 2(1) - 1 = 1
    Now, if we plug in 0 to the even equation we get:
    Even: 2(0) = 0
    If we try it with odd we get:
    Odd: 2(0) - 1 = -1
    Therefore 0 can only be represented by the even equation.

    • Like
    • Report

    3 comments | Post one | Permalink

  • by keithold is a prodigal bagger on March 23rd, 2007

    keithold is a prodigal bagger

    G'day Deemikay,

    Thank you for your question.

    Zero is an even number except in certain circumstances. The definition of an even number is that you can divide it by 2 and not get a remainder. As 0/2 = 0, zero is generally considered to be an even number. However, some people claim that it is neither odd nor even.

    I have attached sources for your reference.

    Regards

    Wikipedia Zero
    http://en.wikipedia.org/wiki/0_%28number%29#Elementary_algebra
    The Straight Dope
    http://www.straightdope.com/mailbag/mzeroeven.html
    Ask Dr Math
    http://mathforum.org/library/drmath/view/57132.html
    Ask Yahoo!
    http://ask.yahoo.com/20020909.html

    • Like
    • Report

    2 comments | Post one | Permalink

  • by mekare on March 23rd, 2007

    mekare

    i think its even because 1 and -1 are both odd

    • Like
    • Report

    3 comments | Post one | Permalink

  • by soar.on.broken.dreams.crystal on March 23rd, 2007

    soar.on.broken.dreams.crystal

    neither

    • Like
    • Report

    11 comments | Post one | Permalink

  • by kanjalid on April 11th, 2005

    kanjalid

    This answer comes from Dr. Hossein Arsham (University of Baltimore): http://home.ubalt.edu/ntsbarsh/Business-stat/opre/ZERO.HTM#revenodd

    Is Zero an Even or Odd Number?

    If one defines evenness or oddness on the integers (either positive or all), then zero seems to be taken to be even; and if one only defines evenness and oddness on the natural numbers, then zero seems to be neither. This dilemma is caused by the fact that the concepts of even and oddness predated zero and the negative integers. The problem posed by this question is that zero is not to be really a number not that it is even or odd.

    Most modern textbooks apply concepts such as "even" only to "natural numbers," in connection with primes and factoring. By "natural numbers" they mean positive integers, not including zero. Those who work in foundations of mathematics, though, consider zero a natural number, and for them the integers are whole numbers. From that point of view, the question whether zero is even just does not arise, except by extension.

    One may say that zero is neither even nor odd. Because you can pick an even number and divide it in groups, take, e.g., 2, which can be divided in two groups of "1", and 4 can be divided in two groups of "2". But can you divide zero? That's why there are so many "questions."

    If you feel that the question if zero is an even number is of no practical value at all, let me quote the following news from the German television news program (ZDF) "Heute" on Oct. 1, 1977:

    Smog alarm in Paris: Only cars with an odd terminating number on the license plate are admitted for driving. Cars with an even digit terminating were not allowed to be driven. There were problems: Is the terminating number 0 an even number? Drivers with such numbers were not fined, because the police did not know the answer.


    A visitor of this site kindly wrote to me that:

    "Is zero odd or even? I suggest a convention, i.e. a useful unproved mechanism which makes me feel better, that zero is indeed Even! I offer two arguments:

    A1: "Odd" numbers are spaced two apart. So are "even" numbers. Proceeding downward, 8,6,4,2,0,-2,-4 .. should all be considered Even. While odd numbers 9,7,5,3,1,-1,-3 ... skip over zero in a most stubborn manner.

    A2: Let two softball teams play a game, with each player betting one dollar a run to the opposing team. Further presume that no runs are scored (due to beer consumption) and no extra innings are allowed because it got dark.

    The final score is zero to zero. If a player is asked by his wife whether he won or lost, he would probably indicate that he "broke even". As the old math teacher said: " Proof? Why any fool can see that."


    These issues make themselves strongly felt in the classroom, textbook, in the frequent mishandling of the notion of zero by the novice and professional alike and therefore recommend themselves to our attention.
    These are among many issues of how to teach these concepts, say, to kids.

    • Like
    • Report

    No comments. Post one | Permalink

  • by Dan Whitacre on December 28th, 2003

    Dan Whitacre

    The definition of "even" from mathworld.wolfram.com:

    An even number is an integer of the form , where k is an integer. The even numbers are therefore ..., -4, -2, 0, 2, 4, 6, 8, 10, ... (Sloane's A005843). Since the even numbers are integrally divisible by two, the congruence holds for even n. An even number n for which also holds is called a singly even number, while an even number n for which is called a doubly even number. An integer which is not even is called an odd number.

    The definition of "zero" from mathworld.wolfram.com:

    The integer denoted 0 which, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) which 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."

    This is from http://mathworld.wolfram.com/CompositeNumber.html, I'd consider them an authority:

    A composite number n is a positive integer n > 1 which is not prime (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes called "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16, ...

    • Like
    • Report

    2 comments | Post one | Permalink

  • by Sid on December 23rd, 2008

    Sid

    Even, as it alternates: 0 1 2 3 4 5/even odd even odd even odd.

    • Like
    • Report

    No comments. Post one | Permalink

  • by Anonymous on September 17th, 2008

    Anonymous

    im here to end everything and tell you that 0 is an even number becuase an even number has always been reffered to as a number divisble by 2 leaving 0 although 0 divided by any number remainder is 0 the fact is that 0 is divisble by without any remainder

    • Like
    • Report

    No comments. Post one | Permalink

  • by Anonymous on April 13th, 2008

    Anonymous

    I will give you no straight answer, so everybody can draw their own conclusion.

    Being Odd or Even is one of the properties of an integer. Zero don't have a property, yet it can assume the property of anything, you can brand it any way you want but it won't stick to it, because there's NOTHING to stick to:
    three girls = females
    seven boys = males
    zero girls = males or females?

    All units of measurements becomes equal at zero:
    zero inches = zero miles
    zero inches = zero volts (amazing)
    zero inches = zero pounds (amazing)

    All objects becomes the same at zero:
    zero gal of water = zero gal of oil
    zero gal of water = zero gal of bytes
    (What? Say that again. I didn't know bytes could be
    measured in gallons. It doesn't matter, it is zero
    anyway)

    • Like
    • Report

    No comments. Post one | Permalink

  • by Why Should I on April 13th, 2008

    Why Should I

    Even. Because anything with an 8, 6, 4, 2, or 0 at the end of it is considered even.

    • Like
    • Report

    No comments. Post one | Permalink

  • by 0null0 on April 13th, 2008

    0null0

    An even number is a number that is exactly two times an integer.

    Is zero an even number?
    Is zero exactly two times an integer?

    Zero is exactly two times zero.
    Therefore, zero is exactly two times an integer (the "integer" in this case being zero).

    Therefore, zero is an even number.

    • Like
    • Report

    No comments. Post one | Permalink

  • by ImNotAnonymous-COAT of Maestro-ness on April 13th, 2008

    ImNotAnonymous-COAT of Maestro-ness

    It's technically even.

    • Like
    • Report

    No comments. Post one | Permalink

  • by Anonymous on April 13th, 2008

    Anonymous

    I believe it is an odd number.

    I read earlier that an even number is a number divisible by two with no remainder, so:

    0/2=0 (no remainder)

    However, :

    0/1=0 (no remainder)

    Above, zero was divided by an odd number and still ended up with no remainder.

    So, I'd like to believe that it is neither even nor odd.


    O.o

    • Like
    • Report

    1 comment | Post one | Permalink

  • by Metaphiz on April 2nd, 2007

    Metaphiz

    After carefully reading the other answers I have decided that "0" is a very odd even number, but "even" all the same.

    • Like
    • Report

    1 comment | Post one | Permalink

  • by Tanshorty on April 1st, 2007

    Tanshorty

    well, zero is concidered to be even because when devided by 2 u get no remainder which is common of even numbers. for example... 4 devided by 2=2

    also if u add an even number it results in an even number...for example 0+2=2

    also consider the pattern of the number line...
    -2 -1 0 1 2
    even odd 0 odd even
    therefore it should be even!

    although some mathamaticians argue that it is neither odd or even because it has special features.

    i hope that answers your question is zero odd or even?

    • Like
    • Report

    No comments. Post one | Permalink

  • by Mister Sister on March 23rd, 2007

    Mister Sister

    Even

    • Like
    • Report

    No comments. Post one | Permalink

  • by swannie on March 23rd, 2007

    swannie

    I think it is even, because it is between -1 and 1, which are both odd.

    • Like
    • Report

    5 comments | Post one | Permalink

  • by Moodles on January 30th, 2005

    Moodles

    I was tought that an even number is one you can divide by 2 and get a number with no decimals - meaning 0 is even. However it is also considered that 0 is the absence of any value/number and is therefore neither even nor odd because it is not an actual number on its own. I believe there will always be a debate as to whether it is even or not, but something I think everyone agrees on is that it is definitely NOT odd! :-)

    • Like
    • Report

    No comments. Post one | Permalink

  • by zerogreen on October 19th, 2003

    zerogreen

    Zero cannot be considered as an even or an odd number. An even number is an number that is dividable by two. Zero is not dividable by two. So it must be neither.

    • Like
    • Report

    5 comments | Post one | Permalink

  • by Mr D @ AGS on April 23rd, 2009

    Mr D @ AGS

    I loved the Paris smog situation!!...with the zero number plates!

    My take: ZERO is an EVEN number BY DEFAULT, because it's placed between -1 and 1 on the whole-numberline!

    It also follows the rules that previous people mentioned in this FORUM.

    Mr D
    Head of Maths
    Alphington Grammar
    Melbourne Australia

    No comments. Post one | Permalink

  • by montanarox101 on May 13th, 2012

    montanarox101

    No comments. Post one | Permalink

  • by esq63 on May 13th, 2012

    esq63

    In some cases zero is considered an " infanite " # wich could be consistant to either greater or less then any other single digit


    Zero is a number; in fact, it is a real number. It is on the number
    line right between 1 and -1. You can add, subtract, and multiply with
    0 and get real answers. You can divide numbers into zero and get a
    real answer, zero.

    You can't say anything like that about infinity. It is not on the
    number line and you can't do computations with it.

    Now, consider 1/0. You know that 1/1 =1, 1/0.1 = 10, 1/0.01 = 100,
    1/0.001 = 1000, etc... Pick a power of 10 as large as you want and I
    can find a number larger than 0 that I can divide into 1 and get your
    number as a result.

    In other words, as we divide numbers into 1 and those numbers get
    closer and closer to 0, the quotient gets larger and larger with no
    boundary. We conclude then, that 1/0 = infinity.

    However, that is just a shorthand notation. Actually, division by zero
    is undefined. It is more precise to say that

    Limit 1/x = oo As x gets closer to zero, the value of 1/x
    x->0 grows without bound (i.e., approaches infinity)

    Unfortunately, often people will use the shorthand, without making it clear
    that this is what's going on. So other people see what they've written, and
    think that '1/0 = infinity' is an actual statement of fact, when it's not.

    In the same way, people will often write '1/infinity = 0', instead of
    the more precise

    Limit 1/x = 0 As x grows without bound (i.e., approaches
    x->oo infinity), the value of 1/x gets closer to 0.

    No comments. Post one | Permalink

  • by Metaphiz on March 23rd, 2007

    Metaphiz

    Odd

    1 comment | Post one | Permalink

  • by montanarox101 on May 13th, 2012

    montanarox101

    No comments. Post one | Permalink

  • by Dennis_O on December 1st, 2010

    Dennis_O

    again..0/1=0
    0/252=0
    0/9 guess what? =0
    its an odd number by def of what everone is saying here and is -1 odd?? rethink please

    No comments. Post one | Permalink

  • by Owl 12 - 12 on October 22nd, 2010

    Owl 12 - 12

    Zero is an even number.

    No comments. Post one | Permalink

  • by Dennis_O on December 1st, 2010

    Dennis_O

    why then is 2 devided by zero undefined? 0 is NOT an even number

    1 comment | Post one | Permalink

  • by BCT555 on October 30th, 2007

    BCT555

    Yes

    No comments. Post one | Permalink

  • by Angie Yo on October 16th, 2003

    Angie Yo

    I always thought is was considered neither because of some junk about it being the origin or absolute or something else...but I'm not an expert. I know I was told that it was either though, I could be wrong.

    4 comments | Post one | Permalink

  • by iwnit on October 10th, 2008

    iwnit

    "The number 0 is even. There are several ways to determine whether an integer is even or odd, all of which indicate that 0 is an even number: it is a multiple of 2, it is evenly divisible by 2, it is surrounded on both sides by odd integers, and it is the sum of an integer with itself. These proofs follow immediately from the definition of the term "even number", which does not allow in zero arbitrarily; it can be further motivated by the familiar rules for sums and products of even numbers. Within the even numbers, zero plays a central role: it is the identity element of the group of even integers, and it is the starting case from which all other even natural numbers are recursively generated. Every integer divides 0, including each power of 2; in this sense, 0 is the most even number of all.
    On the other hand, psychologically speaking 0 is often the least even number of all. In reaction time experiments, most subjects are slower to call 0 even than other even numbers. Both students and teachers in primary education are prone to a common misconception that the parity of zero is ambiguous, or simply that zero is odd. Several researchers in mathematics education write that such misconceptions represent an opportunity for exploration. Class discussions can highlight the necessity of reasoning from agreed-upon definitions. Reviewing sentences like 0 × 2 = 0 can expose students' apprehensions about calling 0 a number and using it in arithmetic. While understanding zero is a worthy end in itself, the particular consideration of parity is an early example of extending a familiar concept to an unfamiliar and perhaps unexpected setting — a pervasive theme throughout mathematics."

    "The precise definition of any mathematical term, such as "even" meaning "integer multiple of two", is ultimately a convention. And unlike "even", some mathematical terms are purposefully constructed to exclude especially trivial or degenerate cases. Prime numbers are a famous example. The definition of "prime number" has historically shifted from "positive integer with at most 2 factors" to "positive integer with exactly 2 factors", with the effect that 1 is no longer considered prime. Most authors rationalize this shift by observing that the modern definition more naturally suits mathematical theorems that concern the primes. For example, the fundamental theorem of arithmetic is easier to state when 1 is not considered prime.
    It would be possible to similarly redefine the term "even" in a way that no longer includes zero. However, in this case, the new definition would make it more difficult to state theorems concerning the even numbers. Already the effect can be seen in the the algebraic rules governing even and odd numbers. The most relevant rules concern addition, subtraction, and multiplication:
    even ± even = even
    odd ± odd = even
    even × integer = even
    Inserting appropriate values into the left sides of these rules, one can produce 0 on the right sides:
    2 − 2 = 0
    −3 + 3 = 0
    4 × 0 = 0
    The above rules would therefore be incorrect if zero were not even; at best they would have to be modified in some way. For example, one test study guide asserts that even numbers are characterized as integer multiples of two, but zero is "neither even nor odd". Accordingly, the guide's rules for even and odd numbers contain some exceptions:
    even ± even = even (or zero)
    odd ± odd = even (or zero)
    even × nonzero integer = even
    Making an exception for zero in the definition of evenness forces one to make such exceptions in the rules for even numbers. From another perspective, taking the rules obeyed by positive even numbers, and requiring that they continue to hold for all integers, forces the usual definition and the evenness of zero."
    Source and further information:
    http://en.wikipedia.org/wiki/Evenness_of_zero

    No comments. Post one | Permalink

  • by Dmitri on December 23rd, 2008

    Dmitri

    Neither, I believe.

    No comments. Post one | Permalink

  • by Anonymous on July 17th, 2008

    Anonymous

    Well, the terms odd and even only applies to postive integers. Therfore, 0, which is not a positive integer cannot be said odd or even.

    No comments. Post one | Permalink

  • by Anonymous on December 3rd, 2007

    Anonymous

    niether i don't know why but on a worksheet i'm doing now i'm trying to find out why zero is not even or odd.

    No comments. Post one | Permalink

  • by Anonymous on April 1st, 2007

    Anonymous

    0 is even.

    No comments. Post one | Permalink

  • by Firebrand on April 1st, 2007

    Firebrand

    Working on a basis of Odd then Even it should be an even number. I believe that it is considered as such

    No comments. Post one | Permalink

  • by Me-Ki-Gal on April 20th, 2010

    Me-Ki-Gal

    0 is and odd number .
    a. 2 is the first even number for if you take away a 1 you get a prime , but to start the matrix of odd numbers you have to start with 0 but 0 is like a pump before it gets primed, so you have to give it a drink of water before it will suck the well dry

    Sampling of sequence:
    0 1 3 5 7
    9 11 13 15 17
    19 21 23 25 27
    29 31 33 35 37
    39 41 43 45 47
    49 51 53 55 57
    59 61 63 65 67
    69 71 73 75 77
    79 81 83 85 87
    89 91 93 95 97
    i hope this is enough to see. O.K.
    3x9= 27
    3x11=33
    is the same relationship in the matrix as
    3x19=57
    3x21=63
    this is the mechanism that makes math work. So 0 is kind of dead so to speak and it does not resurrect until you put in something like the 1 3 5 or 7 or any prime number , but 2 is not prime like some would have you believe, because you have to have 1 + another 1 so the pump was already primed before you get a 2 that is why the 2 is not in the matrix. So in conclusion 0 is like the pump and the numbers are like the water, but with out the pump you ain't getting any water, so it is the the most primary of them all

    1 comment | Post one | Permalink

Want to attach an image to your answer? Click here.

Did this answer your question? If not, then ask a new question or create a poll.

More Questions. Additional questions in this category.

You're reading Is zero considered an even or odd number, or neither? - which can also be phrased in the following ways:

  • Is 0 odd or even?

Follow us on Facebook!

Related Ads

Related Questions

Professionally Researched

ANSWERBAG BUZZ

Is zero an even number
Is 0 an even number
Is 0 even or odd
Is zero odd or even
Is zero even or odd

Answerbag

a Demand Media company