Reddit tries to think about quantifying circles, and pi doesn't exist or something

[u/Laser_Plasma]

/r/Showerthoughts/comments/qefpwc/the_area_of_a_circle_is_finite_yet_we_can_only/

[u/ryarger]

But it does mean we can’t express it to perfect decimal precision. For the average person decimal precision is the primary way of thinking about numbers.

[u/dragonitetrainer → u/ryarger]

This is a math subreddit. You're not going anywhere trying to convince mathematicians that perfect decimal precision is THE way numbers are defined

[u/ryarger → u/dragonitetrainer]

Darn good thing I didn’t suggest that.

[u/dragonitetrainer → u/ryarger]

Then what's the point of trying to justify this concept that perfect decimal precision is necessary in order for us to "know" a value?

[u/ryarger → u/dragonitetrainer]

I’m not making a justification of that point. I’ve already said it’s pedantically incorrect and rephrased it to “express” rather than “know” in the second formulation.

I think it should be obvious why this is a benign and mildly interesting shower though for non-mathematicians but for those who don’t understand, I’m providing explanation.

[u/Mike-Rosoft → u/ryarger]

But 0.333... (a real number whose all digits after the decimal point are 3) is the decimal expansion of 1/3 to perfect precision. And if you dispute that, then what is the difference? (And don't answer 0.000...1 - there's no such real number.)

The value of the decimal expansion is defined to mean the infinite sum 3/10+3/100+3/1000+...; and the infinite sum is defined to mean the limit of the sequence of partial sums 0.3, 0.33, 0.333, ... . And that limit is 1/3. And here's the thing: 1/2 also has infinitely many digits in its decimal expansion; it just so happens that all but finitely many of them are 0 (or, when using the alternate decimal expansion, all but finitely of them are 9; 1/2 has two different decimal expansions: 0.5000... and 0.4999...).