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The even number question and the Earth/Sun question seem subtly different in that I can imagine people knowing that 0/2 = 0, but being unsure if the definition

The even number question and the Earth/Sun question seem subtly different in that I can imagine people knowing that 0/2 = 0, but being unsure if the definition of "even" includes that. (I can imagine they might hazily think "even" requires being twice a positive integer). This isn't the case with the Earth/Sun question. Analogous questions at slightly more sophisticated levels: "Is zero a natural number?" "Is 1 a prime?" "Does an algebraic ring contain the multiplicative identity?" (At least two of those rely on definitions that have been ambiguous at some point.)

capitainenemo 6y ago
Don't you mean definition of even is X%2=0 ? 0%2=0
- CJefferson 6y ago
  Many people think even means "can be divided by two (by which they mean, when divided by 2 the result is an integer). Yes, that is logically equivalent to "x%2=0", but that isn't how (I think) most people imagine it.
  - capitainenemo 6y ago
    I understood what he meant to say (divisible by zero with no remainder - that is, modulus of zero) it was just the equation was surprising. It was technically correct but not useful in context. Otherwise 16/2=0 would fit as well. So figured it was worth clarifying in case anyone else was surprised too. :)
- vmilner 6y ago
  I was (clumsily) trying to say: "know that 0/2 is an integer (i.e. zero), but are not sure if an integer result is enough to qualify 0 as even"
  - capitainenemo 6y ago
    Ah. Gotcha. That makes sense.
raverbashing 6y ago
> "Is zero a natural number?" As with the PEMDAS "trick" questions that show up sometimes on the internet, this is a trick question to what I say: it is what you want to be. Integers/Positive/Rational etc numbers have an exact definition. "Natural numbers" are "numbers that appear in nature" or some finicky definition like that. If you want 0 to be there it's fine. If you don't you're wrong but it's fine as well ;) If you want "positive integers > 0" say that.
- RHSeeger 6y ago
  I am unsure why parent comment is downvoted. Depending on where you looks, 0 may or may not be included in the set of natural numbers. ---- Lexicon / Oxford Dictionary https://www.lexico.com/en/definition/natural_numbers https://www.lexico.com/en/definition/natural_numbers > The positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well. ---- Wikipedia https://en.wikipedia.org/wiki/Natural_number https://en.wikipedia.org/wiki/Natural_number > Some definitions, including the standard ISO 80000-2,begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, ... ---- Math World / Wolfram https://mathworld.wolfram.com/NaturalNumber.html https://mathworld.wolfram.com/NaturalNumber.html > The term "natural number" refers either to a member of the set of positive integers 1, 2, 3, ... (OEIS A000027) or to the set of nonnegative integers 0, 1, 2, 3, ...
- saagarjha 6y ago
  > Integers/Positive/Rational etc numbers have an exact definition. Is zero positive?
  - 6nf 6y ago
    No, hence there is a difference between 'Positive' and 'Non Negative'.
btilly 6y ago
The question, "Is zero a natural number?" is more ambiguous than you think. Back when I was in grad school we informally polled the mathematicians in the department on whether 0 should be a natural number, and got about an even split. The key factor being what area of math you specialized in. So, for example, people studying logic and combinatorics thought it should be because the empty set comes up a lot. But people studying number theory and combinatorics thought it shouldn't because they are always dealing with things enumerated and starting at 1. When I went through school, I was expected to memorize that natural numbers start with 1, and distinguished them from whole numbers that include 0. But this is an entirely arbitrary distinction. As https://en.wikipedia.org/wiki/Natural_number https://en.wikipedia.org/wiki/Natural_number says, there is no general consensus on whether 0 should be included, and there are a variety of unambiguous terminologies that are preferred for cases where it matters.
ummwhat 6y ago
I think I get what is happening with the earth/sun question. If you imagine the earth going around the sun but also not rotating on its axis, then a single trip around the sun would cause a single "day" on Earth. It's still wrong, but at least it is consistent.

capitainenemo 6y ago

Don't you mean definition of even is X%2=0 ? 0%2=0

CJefferson 6y ago
Many people think even means "can be divided by two (by which they mean, when divided by 2 the result is an integer). Yes, that is logically equivalent to "x%2=0", but that isn't how (I think) most people imagine it.
- capitainenemo 6y ago
  I understood what he meant to say (divisible by zero with no remainder - that is, modulus of zero) it was just the equation was surprising. It was technically correct but not useful in context. Otherwise 16/2=0 would fit as well. So figured it was worth clarifying in case anyone else was surprised too. :)
vmilner 6y ago
I was (clumsily) trying to say: "know that 0/2 is an integer (i.e. zero), but are not sure if an integer result is enough to qualify 0 as even"
- capitainenemo 6y ago
  Ah. Gotcha. That makes sense.

raverbashing 6y ago

> "Is zero a natural number?" As with the PEMDAS "trick" questions that show up sometimes on the internet, this is a trick question to what I say: it is what you want to be. Integers/Positive/Rational etc numbers have an exact definition. "Natural numbers" are "numbers that appear in nature" or some finicky definition like that. If you want 0 to be there it's fine. If you don't you're wrong but it's fine as well ;) If you want "positive integers > 0" say that.

RHSeeger 6y ago
I am unsure why parent comment is downvoted. Depending on where you looks, 0 may or may not be included in the set of natural numbers. ---- Lexicon / Oxford Dictionary https://www.lexico.com/en/definition/natural_numbers https://www.lexico.com/en/definition/natural_numbers > The positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well. ---- Wikipedia https://en.wikipedia.org/wiki/Natural_number https://en.wikipedia.org/wiki/Natural_number > Some definitions, including the standard ISO 80000-2,begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, ... ---- Math World / Wolfram https://mathworld.wolfram.com/NaturalNumber.html https://mathworld.wolfram.com/NaturalNumber.html > The term "natural number" refers either to a member of the set of positive integers 1, 2, 3, ... (OEIS A000027) or to the set of nonnegative integers 0, 1, 2, 3, ...
saagarjha 6y ago
> Integers/Positive/Rational etc numbers have an exact definition. Is zero positive?
- 6nf 6y ago
  No, hence there is a difference between 'Positive' and 'Non Negative'.

btilly 6y ago

The question, "Is zero a natural number?" is more ambiguous than you think. Back when I was in grad school we informally polled the mathematicians in the department on whether 0 should be a natural number, and got about an even split. The key factor being what area of math you specialized in. So, for example, people studying logic and combinatorics thought it should be because the empty set comes up a lot. But people studying number theory and combinatorics thought it shouldn't because they are always dealing with things enumerated and starting at 1. When I went through school, I was expected to memorize that natural numbers start with 1, and distinguished them from whole numbers that include 0. But this is an entirely arbitrary distinction. As https://en.wikipedia.org/wiki/Natural_number https://en.wikipedia.org/wiki/Natural_number says, there is no general consensus on whether 0 should be included, and there are a variety of unambiguous terminologies that are preferred for cases where it matters.

ummwhat 6y ago

I think I get what is happening with the earth/sun question. If you imagine the earth going around the sun but also not rotating on its axis, then a single trip around the sun would cause a single "day" on Earth. It's still wrong, but at least it is consistent.