Comment by cloverich 3 months ago
The same logic applies to teachers, and can be applied against your own question.
As an example i once lost a mark on a math test because when rounding to the nearest whole number, i put 3.0 as the answer. Wrong. 3 is a whole number, 3.0 is not i was told, and threatened with suspension on protest. That kind of thing sticks with you.
I agree with your sentiment however, i just dont think its a powerful retort.
Well, you were technically wrong. Which is wrong. var wholeNumber = 3.0; - what type will be assumed for that value?
The class is mathematics. In mathematics, numbers do not have types.
You also shouldn't try to mention INT_MAX, negative zero, rounding error, or other computer science topics which do not exist in mathematics.
Type theory comes from math. Numbers in math do in fact have types. Most of the time we ignore it but numbers in math have types. math also has the concept of max number rolling back to zero ogain something anyone who has studied types in math would know. Rounding error is studied in several different math fields.
negative zero isn't in any math I know of. It is only in obsolete computer science though.
Mathematicians generally work with sets, not types. The first thing you do after defining the reals is agree that the naturals, integers, and rationals are subsets. From a type theory perspective, they are all type ℝ, and, roughly, the naturals satisfy the proposition "n:ℝ is a natural number".
Mathematics has a lot of different theories and some small branches have different rules. I've done mod math for example (it was maybe one week of classes) where you don't get an infinite set of possible numbers. It isn't nearly as interesting as far as mathematicians are concerned (for good reason) so it isn't looked at much but those theories exist.
I am no Terry Tao, but I do have a degree in mathematics. Other than possibly in a class on numerical analysis, I don't remember anything resembling types.
We definitely spent more time discussing different kinds of infinity than we did discussing rounding error!
I can believe that the situation might be different in "applied mathematics" or definitely in "engineering mathematics" - but at least at Berkeley, the latter degree is in the College of Engineering, not under the Math Department at all.
>>> a = 3.0
>>> b = 3
>>> type(a) == type(b)
False
For example, 10 / 3 = 3.333... right? We're then asked to round to the nearest whole number, and the answer should be 10 / 3 = 3. It is not correct to then say 10 / 3 = 3.0, because that is just wrong.
I'd end up siding with the teacher on this one. Just acknowledge you didn't understand what they were looking for and do better next time.
As someone who (almost!) has a PhD in mathematics I'm going to have to call you out on this point. You are thinking like an engineer and talking about precision, but this is mathematics, not engineering. We make no distinction between the "real" number 3, the "complex" number 3, and the "whole" number 3. The number 3 lives in each of these universes as the same object (so to speak) because these sets (whole, real, complex) numbers are included in one another. Writing 3.0 is a representation for 3 just as 2.9999... is a representation of 3. Perhaps the bigger question we should be asking here is what was the purpose of all of this discussion? I've seen such petty treatment by teachers all the time and it always discouraged me from pursuing math until I met professors in university who actually tried to teach us something interesting and beautiful about math. This question could have led in that direction actually with a discussion of different kinds of numbers but unfortunately many math teachers in the US are not capable of this, or are too discouraged by the other craziness in schools to have the energy for such conversations.
"Whole number" means that the mantissa is 0, and is not related to what some random programming language asserts in its representational type system.
Math terms like "whole number" are not defined in terms of the behavior of computer programming languages.
In math, not only are 3.0 and 3 the same thing, but also, so is 2.9999999...
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> They weren't looking to see if you knew the arithmetic with that question, they wanted you to show you understood what they meant by "whole number" and understand you can't just leave arbitrary precision after rounding.
Can you show any math reference that supports this viewpoint? This goes against my college mathematics training.
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> You didn't give the right answer
According to mathematics, 3.0 and 3 are the same thing (and so is the Roman numeral III, and so on.) So is 6/2.
It is deeply and profoundly incorrect to treat an answer as incorrect because the mantissa was written out.
The teacher is simply incorrect, as are you.
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> Just acknowledge you didn't understand what they were looking for and do better next time.
If a teacher asks "what is the country north of Austria," in an English speaking school, and you write "Germany," and the teacher says "no, it's Allemande," they're just incorrect. It doesn't matter if the teacher is French. There are only two ways to look at this: either the correct answer is in the language of the school, or any international answer is acceptable.
A normal person would say "oh, ha ha, Germany and Allemande are the same place, let's just move forwards."
A person interested in defeating and winning, instead of teaching, might demand that the answer come in in some arbitrary incorrect format that they expected. That's a bad teacher who doesn't need to be listened to.
Yes, we know there's also some kid who is explaining to just do as teacher instructs, but no, we're there to learn information, not to learn to obey.
> Can you show any math reference that supports this viewpoint? This goes against my college mathematics training.
> The word integer comes from the Latin integer meaning "whole" or (literally) "untouched", from in ("not") plus tangere ("to touch"). "Entire" derives from the same origin via the French word entier, which means both entire and integer.[9] Historically the term was used for a number that was a multiple of 1,[10][11] or to the whole part of a mixed number.
https://en.m.wikipedia.org/wiki/Integer
The question was to understand the idea of a "whole number" aka an integer.
It's very clear you're out of your element on this, and you have multiple people with an actual math background telling you the objection is somewhere between meaningless and wrong.
The takeaway from trying to really nail down a definition of "integers" (or anything, really) is going to be something along the lines of "if it quacks like a duck up to unique isomorphism, it's a duck". The encoding is not important and one frequently swaps among encodings when convenient. In any case, no one who knows any math is going to say to a child that 3 and 3.0 aren't interchangable outside of some extremely specific contexts. In fact that's not even encoding: it's notation. They can be literally equal, not just equivalent. Those particular contexts aren't ordained, and e.g. propagation of uncertainty is "better" than significant figures if you're doing engineering anyway.
Writing something like '10/3=3' is likely to trigger the mathematicians because lots of people get confused about what '=' is supposed to mean (and often use it to mean something like "next step indicator"). '3=3.0' not so much.
> adding that .0 implies a precision which is not correct. They weren't looking to see if you knew the arithmetic with that question, they wanted you to show you understood what they meant by "whole number" and understand you can't just leave arbitrary precision after rounding.
If you round 3.05 down to 3, 3.00 is not arbitrary precision, its explicit precision that's reflective of the rounding operation you did. I wasn't claiming that `type(3.0) == type(3)`. I was claiming that:
>>> round(3.0) == 3
True
It's incredible despite multiple additional individuals telling you that you're wrong you continue doubling down on it.
10 / 3 != 3.000000000000000000000000 no matter how many times you refute it. You should really learn to accept it and continue on and look deeper inside yourself into this. It's sad you still haven't learned this lesson from elementary education. Maybe they should have suspended you.
In no world does 10 / 3 = 3.0. This is just a falsehood as much as 2 + 2. = 5. I don't care about your large values of 2.
'10/3 = 3' is also false, and is something you put forward as true. Meanwhile, '10/3 ≈ 3' and '10/3 ≈ 3.0' are both equally true, as is '10/3 ≈ π' if you're in a pinch. Also true is that math is full of conventions, and it makes sense to use the conventions you feel are appropriate for what you're doing. Sometimes that might be significant figures, which I suppose you're alluding to. Other times, it might be propagation of uncertainty. Other times error tracking is not even relevant; you might just round the thing but also want to have all of your expressions be of the same type. For that matter, you may have 3: ℝ = 3.0: ℝ by definition. The other poster never gave any indication of whether or why some particular convention should apply.
Teachers not having the time to muse about such ideas and instead needing to package everything into a presentation appropriate for an entire room full of children is one of the more obvious failure modes of industrialized education.
> As an example i once lost a mark on a math test because when rounding to the nearest whole number, i put 3.0 as the answer. Wrong. 3 is a whole number, 3.0 is not i was told, and threatened with suspension on protest. That kind of thing sticks with you.
I got threatened with suspension on protest once. It was about the meaning of a word, but still.
Luckily, I'm a university brat, so I just waited a couple days until my dad was keeping me at his office, then I wandered down the hall, and I asked some professors for a detailed and referenced way to push back. I brought candy and tums, because that's what professors want from children who can't bring beer.
About a week later, I went in with a 30 page computer printed essay. As a nine year old. It had six phone numbers in the back, four to PhDs, which could be called for further detail if needed. It was addressed to both the teacher and the principal.
An opening note was "please look into how Marilyn vos Savant was treated when she explained the Monty Hall problem, when considering whether teachers are permitted to threaten students for disagreeing politely. Are you really so afraid of being incorrect?," written by an internationally renowned mathematician.
I was carrying an etymological breakdown that to this day I can barely read, stretching all the way back to the hypothetical proto-indo-european roots.
Professors don't like kids being threatened.
I did not hear about that teacher doing that again while I was in that school.