r/MathHelp • u/Warm_Knowledge4020 • 2d ago
Homework said, “The absolute value of an integer is ALWAYS positive.” My son answered False but was marked wrong. Since 0 is an integer and |0| = 0, and 0 is neither positive nor negative, shouldn’t False be correct? Wouldn’t it need to say “any nonzero integer” to be true?
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u/Toeffli 1d ago
Are you in a French influenced country? There 0 is negative and positive which means the statement would be correct.
If not, the correct statement which includes zero is "The absolute value of any integer is always not negative".
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u/Remarkable_Job_9974 1d ago
I had not heard of this before. Interesting.
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u/rb-j 1d ago
I haven't either.
I think actual mathematicians agree that 0 is neither positive nor negative. Doesn't matter what country they come from.
The correct and concise statement is:
“The absolute value of any real number is ALWAYS nonnegative.”
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u/AcellOfllSpades Irregular Answerer 1d ago
It's definitely a thing. In French, the word "positif" is interpreted to include zero, and same for "négatif".
So "positif" numbers are what we in English would call "nonnegative". And zero is neither positive nor negative, but it's both positif and négatif.
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u/rb-j 1d ago edited 1d ago
Yes, I guess it's true that zero is both nonnegative and nonpositive. I guess I hadn't thunk about it that way.
If I was a French engineering prof, I would likely warn against the usage of "positif" and "négatif" and refer to the English terms for positive and negative (along with nonpositive and nonnegative).
I mean mathematical communication should be concise and unambiguous and I would hate to always have to say "positive in the English sense" or "greater than zero". When the word is "positive" we all should know that zero is not included.
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u/Syharhalna 17h ago
In French “positif” means >= 0 and “strictement positif” (strictly positive) means > 0.
Same things for negative.
Actually, the english version nonnegative for > 0 is quite convoluted because it involves a negation…
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u/DrJaneIPresume 12h ago
Actual mathematicians generally define their terms.
The most common anglophone convention is called the "trichotomy": all real numbers are either positive, negative, or zero.
In more advanced texts that don't explicitly define it, they also don't tend to use "positive" and "negative" as formally. When speaking formally, they'll generally say something like, "let ε be greater than 0".
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u/XenophonSoulis 1d ago
In the English-speaking world, your son is correct. However, in different places the definition of "positive" may be different. In French, a positive number is ≥0.
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u/regular_hammock 1d ago
Correct. We would say ‘strictly positive’ for the English ‘positive’.
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u/dexthefish 1d ago
I like that convention. Although I'm used to the word nonnegative, I think it's linguistically awkward and avoid using it with my younger students.
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u/Lower_Cockroach2432 23h ago
To avoid ambiguity I personally call those non-nonpositive numbers myself.
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u/rb-j 1d ago
They don't have the concept of "nonnegative" in France?
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u/gowipe2004 1d ago
Nonnegative would be strictly positive
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u/vgtcross 1d ago edited 1d ago
You got it backwards.
English "nonnegative" is French "positive"
English "positive" is French "strictly positive"Edit: Maybe you meant that French "nonnegative" is equivalent to French "strictly positive", which true since French "negative" is (-inf, 0] so "nonnegative" would be (0, inf) which is French "strictly positive"
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u/gowipe2004 1d ago
Indeed, what I meant is that for us, nonnegative would mean/equate stricly positive
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u/RecognitionSweet8294 1d ago
Depends on the definition of „positive“.
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u/Andrew1953Cambridge 1d ago
.. and of "integer". Maybe the teacher thinks that integer means "non-zero natural number".
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u/Temporary_Pie2733 1d ago
I hope not. The whole point of the integers is that they every integer has an additive inverse; it makes no sense to use “integer” as a term that excludes half of them.
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u/Andrew1953Cambridge 8h ago
Oh, I agree, but since the teacher doesn't seem to understand standard terminology, who knows what they think.
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u/KiwasiGames 1d ago
Depends on the local definition of positive.
I typically see zero included in the positive numbers.
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u/rb-j 1d ago
Not in math.
Maybe with twos-complement numbers in computer arithmetic. Zero and the positive integers have a leading "0" bit on the left. Only negative numbers have a leading "1" bite on the left.
But the terms "positive" and "nonnegative" are not synonymous. And inclusion of 0 is the difference.
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u/StructuredChess 1d ago
False is the correct answer and that's why this type of True/False or multiple choice questions are terrible ways to measure anything that has even the slightiest amount of nouance.
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u/LordTengil 1d ago
Son is correct, but...
It depends a bit in what system you are. If you are in the french system, or a school system derived thereof, they define 0 as both a positive and a negative, and then they are correct.
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u/CoachSevere5365 1d ago
Wikipedia has a good article on this. Zero is often considered to be positive. In floating point arithmetic positive and negative zeroes exist.
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u/particlemanwavegirl 1d ago
The more I learn about them the more convinced I am that floating points aren't numbers.
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u/Temporary_Pie2733 1d ago
Formally, they are a subset of the rationals with power-of-two denominators, extended with additional values added to handle certain arithmetic operations.
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u/Snezzy_9245 1d ago
The PDP-7 computer of distant memory used one's complement arithmetic and thus had both a positive zero and a negative zero. But surely the teacher wasn't programming 60 years ago. ?
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u/susiesusiesu 1d ago
this is correct.
there are places (like france) where the conventiom is positif and négatif include zero, in opposition to english where positive and negative exclude zero. so, if your son is recieving a non-english education, this may be just a misscommunication.
however, as stated in english, your son is right.
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u/MathsSur64Cases 1d ago
beaucoup de bêtises lue ici : La relation d'ordre par défaut est réflexive : 0 est plus grand que 0. on note 0 ≥ 0 et |x| ≥ 0
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u/edderiofer 1d ago
In English, "greater than" means >, not ≥. The latter is called "greater than or equal to".
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u/GaryHornpipe 1d ago
I thought 0 was positive, and also negative because 0 = -0. But reading the comments, I’m wrong.
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u/Ericskey 1d ago
Positive is not the same as non-negative. That is why we have different words in English at least
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u/Samstercraft 22h ago
correct but definitions can vary by location. in english 0 is not positive. the question should have said "always nonnegative"
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u/localizeatp 18h ago
yes, and well done, kid. please let me know how that teacher took being corrected.
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u/Striking-Milk2717 17h ago
Low school homework are full of gray-zone mathematical error. That’s a good, because this way the average kid will grasp the concepts, but the smart kid will think about it until he finds out the whole thing and grows
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u/Sea-Sort6571 13h ago
Depends on your country. In mine, 0 is an integer and it's positive. I know some English speaking have other nonsensical conventions
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11h ago
[deleted]
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u/edderiofer 10h ago
https://en.wikipedia.org/wiki/Integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...).
The reason "everyone seems to be missing this" is because you're wrong.
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u/ElegantPoet3386 2d ago edited 2d ago
Yeah, your logic is correct. Positive numbers quite literally are defined to be greater than 0 and 0 is not greater than 0. The correct statement is it’s always non negative, which isn’t the same thing as positive.