0 is considered an even number,
but if 0 would be an even number,
then 0 apples would count an even number of apples.


 3 apples [🍏🍏🍏]  
 2 apples [🍏🍏  ]  
 1 apple  [🍏    ]  
 0 apples [      ]  

Can we see 0 apples counting an even number of apples?

Is this of some kind of sophism example considering 0 to be even?

  • 2
    What issue do you see with 0 apples being considered an even number of apples? I don't see the problem. That sounds reasonable enough to me.
    – NotThatGuy
    Commented Sep 28, 2023 at 22:38
  • I don't see 0 counting any apples. I guess in your logic then 0 isn't even a number?
    – JonathanZ
    Commented Sep 29, 2023 at 4:59
  • Numbers being instruments to count things is a nice feature, but not the core of what a number is. Whether or not "zero apples" is a legitimate amount of apples isn't relevent to 0 being even. An integer X, is even if X = 2*Z for some integer Z. As, 0 = 2*0; 0 is by definition an even number. Note: I can't have π many apples, and yet Math would be bereft if we needed to exclude numbers like π because we can't count apples with it. Commented Sep 29, 2023 at 18:09
  • I wrote an article regarding this subject. Sharing as is, maybe interested. Your suspect is resonable.
    – user71091
    Commented Jan 19 at 15:54

3 Answers 3


If you are taking sophism to mean a type of fallacy, then no.

The extension of even numbers from outside the naturals to the non-negative integers is an example of a technical definition in mathematics. Math systems like PA, are examples of formal systems, and formal systems are built on axioms. If one considers the trichotomy property of the integers, where a number is negative, positive, or zero, to maintain closure, one has to deal with the pesky case of zero. (Think of the definition as a z/2 must be in Z.) Obviously, for positives and negatives, to define a double of an integer as zero is fairly intuitive. For any double which is positive or negative, dividing by two results in another positive or negative respectively. But what should be done with zero? It just so happens that because zero occurs before and after an odd number, it just makes sense consider it even, since it is divisible by two. In this way, the formula 2z is closed.

The idea that mathematical systems are built up from axioms is central to mathematical constructivism (SEP), and finding axioms to make systems functional or better is known as reverse mathematics. You may hear terms like abstract objects or fictions thrown around in nominalist (SEP) or fictionalist mathematical (SEP) thinking. This is in distinction to Platonic reasoning about mathematics which tends to see numbers as real or important to identify with real entities. More modern thinking defines numbers not as names to corresponding to counts, but more abstractly like iterations of the successor function.

  • The most often argument for "0 is even" is the expression 2 * 0 = 0. But, if 2 * 0 = 0 demonstrate that "0 is even", because by induction and relation equivalence 13 * 0 = 2 * 0, resulting 13 * 0 = 0 also must demonstrate that "0 is even". Otherwise, if 13 * 0 = 0 does not demonstrate that "0 is even", by induction and equivalence of relation 13 * 0 = 2 * 0, resulting 2 * 0 = 0 also does not demonstrate that "0 is even". Is that self evident or no? The Wikipedia say that "2 * 0 = 0 + 0" demonstrate that "0 is even".
    – user71091
    Commented Jan 24 at 8:55
  • If Wikipedia and others using this argument 2 * 0 = 0 + 0 to demonstrate "0 is even", that means they count an even number of zeros in a sum of zeros to demonstrate "0 is an even number of units 1 in a sum of units 1". They like do not think mathematics, but kind of "evasive politics" or "derutes".
    – user71091
    Commented Jan 24 at 8:58
  • @VitalieGhelbert Wikipedia is merely reporting the convention decided by mathematicians to define 0 as even for consistency and parsimony.
    – J D
    Commented Jan 24 at 15:23
  • This is what I responded to Math Stack. i.sstatic.net/yiUGb.jpg
    – user71091
    Commented Jan 25 at 9:53
  • I was blocked because I asked the following question on math stack: Why odd and even integers have same cardinality, if zero is considered even?. Odd and even integers can have same cardinality exclusively only if zero is considered to have neutral parity, meaning neither odd nor even.
    – user71091
    Commented Jan 25 at 10:26

Start with any even number. Adding/subtracting 2 should take you to the next higher/lower even number.
8 - 2 = 6, 6 - 2 = 4, 4 - 2 = 2, 2 - 2 = 0. O is an even number.

Doing the same for odd numbers you get ...
7 - 2 = 5, 5 - 2 = 3, 3 - 2 = 1, 1 - 2 = -1. 0 is not an odd number.


If one is still unsure, we can always specify the domain like so:
a) 0 is the first even whole number and 1 is the first odd whole number.
b) 1 is the first odd natural number and 2 is the first even natural number

The issue, it seems, is our starting point (0 or 1).



Any integer counts a number of units 1.
The number of units is odd, if divisible by 2 with remainder.
The number of units is even, if divisible by 2 without remainder.
Zero counts zero units 1, therefore 0 has neutral parity, neither odd nor even.

  • This ia false. Zero is an even number. An Integer x is even if it can be written as a product of 2 and another integer y. As 0 can be written as 2*0; 0 is even. What you might be thinking of is signs. 0 is neither positive nor negative Commented Sep 29, 2023 at 18:06
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  • Conclusion: Virgin Mary is The Nature as whole and entire Universe, where Jesus Christ is Logos expressing all meanings of Absolute Knowledge from The Universe.
    – user71091
    Commented Jan 25 at 15:55

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