[jmalicki]

.125 + .375 == .5

You should be using == for floats when they're actually equal. 0.1 just isn't an actual number.

[emil-lp]

Are you saying that my students should memorize which numbers are actual floats and which are not?

    > 1.25 * 0.1
    
    0.1250000000000000069388939039

[jmalicki]

> Are you saying that my students should memorize which numbers are actual floats and which are not?

Yes.

[stephencanon]

Your students should be able to figure out if a computation is exact or not, because they should understand binary representation of numbers.

[jmalicki]

(Another small note.... 1.25 * 0.1 is not representable because 0.1 is not representable, so that doesn't divide by 10)

1.25 = 2^0 + 2^-2, so is representable.

0.125 = 2^-3, so is representable

1.25 / 10.0 = 0.125 so is representable. 10.0 = 2^3 + 2^1.

1.25 * 0.1 is not representable, because 0.1 is not representable, and those low order bits show up in the multiplication

[SideQuark]

If they were taught what was representable and why they’d learn it quickly. And those that forget details later know to chase it down again if they need it. Making it voodoo hides that it’s learnable, deterministic, and useful to understand.

[dehrmann]

Tell them that they can only store integer powers of 2 and their sums exactly. 2^0 == 1. 2^-2 == .25. Then say it's the same with base 10. 10^-1 == 0.1. 1/9 isn't a power of 10, you you can't have an exact representation.

[kccqzy]

They shouldn’t “memorize” this per se, but it should take them only a few seconds to work out in their head.

[Sharlin]

> 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?

[SideQuark]

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.

[Sharlin]

I’m not sure if you got my joke but I referred to the mathematical philosophy, finitism.

[1718627440]

That's essentially what you already do for integer arithmetic.

[tux3]

0.1 is of course a real number, but let A \in R the set of actual numbers... (/s)

[Sharlin]

The funny thing is, according to infinitists real numbers are not real. But I do like the concept of the set of actual numbers.

[hnfong]

I don't know whether I'm an infinitist, but I personally think "real numbers" is the most ingenious marketing term created by mathematicians...

[jmalicki]

\infty is an actual number not in R

[JohnKemeny]

Should be \subset.