/sci/ - Science & Math

>>11955857
>convergence of functions, even uniform, doesn't imply convergence of derivatives

That's right. Therefore you CAN'T assume that a series such as:
.9
.99
.999
.9999
.99999

...will have 1 as its conclusion. There simply is no "conclusion" to this, just like there is no "last nine" at the end of .999...

Pictured: Line BW has a slope of 0. Line BZ has an infinitesimal slope. They are clearly different lines that arrive at different points, and only intersect at 0,0.

>>11945617
>0.3 * 3 = 1
0.3 * 3 = .9

>>11749752
>Why do brainlets refuse to accept that 0.999... = 1?

Because it isn't. I show people the proof in the pic, and they would rather argue that 0=1 than admit that they were wrong. The Real set was INVENTED as a method of ignoring infinitesimals. Therefore any argument using the Real set to claim that 0.999... = 1 is circular logic.

The last time I posted this pic, someone responded that Z and W were the same point, and thus .999...=1. I pointed out that this also made 0=1 and they didn't seem to see why that would be a problem, given that they got the answer they wanted!

What is the slope of line BZ?
How is it different from line BW?

Note that if you try to claim that line ZW is meaningless or doesn't exist somehow, then neither does .999...

>>11485498
>What do you write instead of the "?"?

Let me turn that example back at you. The other infamous "proof" that this is paired with makes the opposite assumption:

1 .9
2 .99
3 .999
4 .9999
5 .99999
6 .999999
...
? .999...

What do you write instead of the "?"?

In the .000...1 example, you say that expression is meaningless because you can't assign it a natural number. But .999... can't be assigned a natural number in this format either. I see this alot in these discussions. "Infinity only works when we want it to." There is just no rhyme or reason to how infinity is applied.

>>11484497
>You can’t have infinitesimals given the usual construction of the reals.

And you can't have fractions given the usual construction of the naturals. That doesn't prove that 1/2 doesn't exist. It is obnoxious to insist that the discussion take place in a number set that is DESIGNED to omit the correct answer.

>>11331532

If .999.. = 1 then 1=0.

In this construction, .999... can not possibly equal 1, because if it did, then line BZ would intersect W, thus proving zero also equals one. Reductio ad absurdum.