/sci/ - Science & Math

>>11538660
[math]0.999...=1 \\ \frac{1}{\infty}=0 \\ \infty \notin \mathbb{N} \\ \infty > \text{TREE(3)}[/math]
i'm glad i can ignore all this retarded shit then.

>>11523123
>haha calculator print long number brrrr

[ 1 ], [ ÷ ], [ 3 ], [ = ]
[ 0 . 3 3 3 3 3 3 3 ]

but in real math, [math]\frac{1}{3} >
0.333\dots [/math]

>>11508483
wow retard.
>>11508148

How mad would atheists be if they learned that math both allows and adheres to unfalsifiable truths?

infinity is unfalsifiable.

>>11499837
>well trained retards do not agree with me therefore its not true
coomthink

>>11499840
Yea but in base 10, 1/3 converted from fractional to decimal is a repeating number. Or rather, [math]\frac{1}{3} > 0.\overline{333}[/math] because there is no direct equality, in decimal.

I think ya'll need to take a step back and realize that decimal and fractional are two different languages and not merely equations vs answers. They might be two very similar languages, but they're not the same, and fractional has easy ways to express a value ([math]\frac{1}{3}[/math]), while decimal has no way to express that same value and must settle for less on [math]0.\overline{333}[/math].

I'm bringing this up because the identity of that value in decimal leads thlo the common misconception/autocorrection of
>[math]\frac{1}{3} = 0.\overline{333} [/math]
>[math]3(\frac{1}{3}) = 3(0.\overline{333}) [/math]
>[math]\frac{3}{3} = 0.\overline{999} [/math]
>and thus 0.999... = 1
But again, 1/3 isn't the only identity in "0.333..." or, multiplied, "0.999..."

to covey this easier, imagine there was a value we could add onto the decimal 1/3 so that it cleanly and completely equals the fractional with nothing lost in translation, let it be
>[math]\frac{1}{3} = 0.\overline{333}_4[/math]
and assume the arithmatic is understood such that
>[math]\frac{3}{3} = 0.\overline{999}_{4×3>10} =
1.0 [/math]

But then take [math]\sum_{n=1}^{\infty} \frac{3}{10^n}[/math], and see it print out a different identity in solely just [math]0.\overline{333}[/math] with no extra bit required to "equal" like 1/3 needed.
The direction of the sum to reach equality is to solely print 3's, while the direction of the conversion of 1/3 to decimal equality requires an extra bit, comparing
>[math](\frac{1}{3} = 0.\overline{333}_4) > (\sum_{n=1}^{\infty} \frac{3}{10^n} = 0.\overline{333})[/math]

and this refocuses the issue from the actual math involved to the reasoning behind whether or not "infinity" is valid.