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>>> a = 3.0 >>> b = 3 >>> type(a) == type(b) False The right answer they were looking for was 3, not 3.0. Adding that .0 implies a precision which is not

>>> a = 3.0 >>> b = 3 >>> type(a) == type(b) False The right answer they were looking for was 3, not 3.0. 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. You didn't give the right answer and apparently kept complaining about it instead of trying to figure out why you were wrong to the point they threatened suspension. I imagine your complaints based on your assumption you couldn't be wrong were causing quite a distraction. 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.

cloverich 2y ago
> 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 And that such a representation was valid within the context of the question. This was long before I was wise enough to understand that sir, this is a public school, just do what the book says and don't make me talk with the students more than I need do.
- vel0city 2y ago
  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.
  - ndriscoll 2y ago
    '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.
    - vel0city 2y ago
      [flagged]
      - ndriscoll 2y ago
        '10 / 3 = 3' is either bad notation or wrong. It's not true under any usual definition of 10, 3, / or =. '3 = 3.0' on the other hand is perfectly reasonable in many circumstances. If you think 10/3 can equal 3 but not 3.0, you are either confused or confusing or both. What you mean to write is '≈', and when you do that, it's obvious that 3 and 3.0 are both usable in that sentence. It is perfectly reasonable to define 3: ℕ = succ(succ(succ(zero))). It's also perfectly reasonable to define 3: ℝ as the image of succ(succ(succ(zero))): ℕ under the canonical embedding. Or you can define 3: ℚ with the obvious element. You can also define 3.0: ℚ or 3.0: ℝ as the obvious elements. If you were really a deviant, I suppose you could even define 3.0: ℕ, and people would roll their eyes, but everyone would understand you. Obviously, there are reasonable ways to define things so that `3 = 3.0` is a meaningful sentence (typechecks) and also literally true. Again, different conventions are used in different contexts. The "user" of mathematics should pick the conventions and notations that make sense for what they're doing to communicate what they're trying to say. That itself is an important lesson. The sigfig convention you learned in middle school isn't the word of God. Not being aware of these things to be capable of musing about them is I suppose another issue with our education system.
JohnHaugeland 2y ago
"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... . > 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. . > 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. . > 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.
- vel0city 2y ago
  > 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 https://en.m.wikipedia.org/wiki/Integer The question was to understand the idea of a "whole number" aka an integer.
Gabriel54 2y ago
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.

cloverich 2y ago

> 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 And that such a representation was valid within the context of the question. This was long before I was wise enough to understand that sir, this is a public school, just do what the book says and don't make me talk with the students more than I need do.

vel0city 2y ago
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.
- ndriscoll 2y ago
  '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.
  - vel0city 2y ago
    [flagged]
    - ndriscoll 2y ago
      '10 / 3 = 3' is either bad notation or wrong. It's not true under any usual definition of 10, 3, / or =. '3 = 3.0' on the other hand is perfectly reasonable in many circumstances. If you think 10/3 can equal 3 but not 3.0, you are either confused or confusing or both. What you mean to write is '≈', and when you do that, it's obvious that 3 and 3.0 are both usable in that sentence. It is perfectly reasonable to define 3: ℕ = succ(succ(succ(zero))). It's also perfectly reasonable to define 3: ℝ as the image of succ(succ(succ(zero))): ℕ under the canonical embedding. Or you can define 3: ℚ with the obvious element. You can also define 3.0: ℚ or 3.0: ℝ as the obvious elements. If you were really a deviant, I suppose you could even define 3.0: ℕ, and people would roll their eyes, but everyone would understand you. Obviously, there are reasonable ways to define things so that `3 = 3.0` is a meaningful sentence (typechecks) and also literally true. Again, different conventions are used in different contexts. The "user" of mathematics should pick the conventions and notations that make sense for what they're doing to communicate what they're trying to say. That itself is an important lesson. The sigfig convention you learned in middle school isn't the word of God. Not being aware of these things to be capable of musing about them is I suppose another issue with our education system.

JohnHaugeland 2y ago

"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... . > 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. . > 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. . > 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.

vel0city 2y ago
> 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 https://en.m.wikipedia.org/wiki/Integer The question was to understand the idea of a "whole number" aka an integer.

Gabriel54 2y ago

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.