[librasteve]

when I was a kid in junior school, I was taught that 0.1 means 1/10 something like the . is a division sign, digits to the right are the numerator and the denominator is the position of the digit to the power of 10

true, in fact the syntax of Python consumes the literal '0.1' as a double [float64] ... so ok maybe I was a bit strong that my fact trumps the Python fact (but it still feels wrong to say that 0.1 + 0.2 > 0.3)

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I welcome your correction on FatRat ... btw I have just upgraded https://raku.land/zef:librasteve/Physics::Unit to FatRat. FatRat is a very useful string to the bow and imo cool that it's a core numeric type.

See also https://raku.land/zef:librasteve/FatRatStr as my path to sidestep P754 literals.

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We are on the same page that the Rat compromise (degrade to P754) is optimal.

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As you probably know, but I repeat here for others, Raku has the notion of https://docs.raku.org/language/numerics#Numeric_infectiousne... which means that `x + 1/3' will return a Rat if x is an Int or a Num if x is a Num. All "table" operators - sin , cos, log and so on are assumed to return irrationals (Num).

[eesmith]

You likely also learned in school that some calculators do left-right evaluation while other, more expensive ones, do PEMDAS. And a few do postfix instead. You might also have learned that most calculators didn't handle 1/3 as a fraction, in that 1 / 3 * 3 is 0.99999999.

Python is a fancy calculator.

To be clear, while in the mathematical sense, yes, sin, cos, and log generally return irrationals, in their IEEE 754 forms they return an exact value within 1 ulp or so of that irrational number. Num is a rational. ;)

  >>> x=5**0.5
  >>> x
  2.23606797749979
  >>> x.as_integer_ratio()
  (629397181890197, 281474976710656)

Scheme uses the phrase "numerical tower" for the same sort of implicit coercion.

[eesmith]

I just realized that in school you likely also learned that 1.0 and 1.000 are two different numbers for physical measurements as the latter implies a higher measurement precision.