Comment by cloverich

Comment by cloverich 3 months 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 3 months 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.

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ndriscoll 3 months 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.

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- vel0city 3 months ago
  
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  ndriscoll 3 months 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.
  
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  JohnHaugeland 3 months ago
  
  > 10 / 3 can = 3, depending on the expected levels of precision.
  >
  > 10 / 3 will never = 3.0.
  You should read what they wrote again. They wrote with `≈`, which is a different operator than `=`.
  What they wrote is correct.
  .
  > It is sad you still haven't learned this lesson after many decades.
  >
  > I hope I'm never on a bridge you build or plane built to the specs you write if you truly think 10 / 3 = 3.00000.
  HN doesn't allow this sort of behavior.
  
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