Comment on What every computer scientist should know about floating-point arithmetic (1991) [pdf]parentComments−Sharlin5mo 0.1 just isn't an actual number.A finitist computer scientists only accepts those numbers as real that can be expressed exactly in finite base-two floating point?−SideQuark5moYes. A computer scientist should know how numbers are represented and not expect non-representable numbers in that format to be representable.0.1 is just as non-representable in floating point as is pi as is 100^100 in a 32 bit integer.Terminating dyadic rationals (up to limits based on float size) are the representable values.−Sharlin5moI’m not sure if you got my joke but I referred to the mathematical philosophy, finitism.−17186274405moThat's essentially what you already do for integer arithmetic.−tux35mo0.1 is of course a real number, but let A \in R the set of actual numbers... (/s)−Sharlin5moThe funny thing is, according to infinitists real numbers are not real. But I do like the concept of the set of actual numbers.−hnfong5moI don't know whether I'm an infinitist, but I personally think "real numbers" is the most ingenious marketing term created by mathematicians...−jmalicki5mo\infty is an actual number not in R−JohnKemeny5moShould be \subset.
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A finitist computer scientists only accepts those numbers as real that can be expressed exactly in finite base-two floating point?
Yes. A computer scientist should know how numbers are represented and not expect non-representable numbers in that format to be representable.
0.1 is just as non-representable in floating point as is pi as is 100^100 in a 32 bit integer.
Terminating dyadic rationals (up to limits based on float size) are the representable values.
I’m not sure if you got my joke but I referred to the mathematical philosophy, finitism.
That's essentially what you already do for integer arithmetic.
0.1 is of course a real number, but let A \in R the set of actual numbers... (/s)
The funny thing is, according to infinitists real numbers are not real. But I do like the concept of the set of actual numbers.
I don't know whether I'm an infinitist, but I personally think "real numbers" is the most ingenious marketing term created by mathematicians...
\infty is an actual number not in R
Should be \subset.