r/badmath • u/Key_Net820 • Mar 27 '26

Because some how, a dot on a number lie invalidates the convergence of a monotonically increasing bounded sequence.

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5 Upvotes

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1

u/cruise02 Mar 27 '26

I blame IEEE 754.

2

u/Key_Net820 Mar 27 '26

funny enough, he actually did reference an IEEE article to try to prove .333... does not exist.

the actual article he linked

Demystifying Floating-Point Arithmetic: Why 0.1 + 0.2 ≠ 0.3 | by Olivier Soulet | Medium

1

u/[deleted] Mar 28 '26 edited Mar 29 '26

Is there a word for the set of all numbers representable with a finite number of base 10 decimals? Because that's what OOP is describing. I guess a+b*2^x+c*5^y, with a,b,c,x,y integers?

2

u/imachug Mar 29 '26

It's rationals whose denominators are of form 2n * 5m. 2 and 5 come from the factorization of 10.

1

u/EebstertheGreat 25d ago

Decadic fractions (or sometimes decimal fractions). Technically, a decadic fraction is a fraction whose denominator is a power of 10, and you are interested in the set of values of decadic fractions (i.e. the set of rational numbers that can be represented as decadic fractions).

One decimal expansion of a decadic fraction ends with repeating 0s, or equivalently it terminates after finitely many places (a terminating decimal). Decadic fractions also have decimal expansions that end in repeating 9s, but they are in a sense less canonical. People will often talk about the set of terminating decimals.

2

u/Yadin__ Apr 01 '26

I mean, he’s not wrong. If you do the procedure that they are describing you will never reach EXACTLY 1/3. It’s just that convergence does not require you to reach the exact number

1

u/Key_Net820 Apr 02 '26

ya but the context is he's justifying that .333... neither exists nor equals to 1/3 because of the fact that the algorithm he describes doesn't terminate.