/sci/ - Science & Math » Thread #12350175

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Anonymous Mon 16 Nov 16:41:50 2020 No.12350175 View Reply Original Report

Quoted By: >>12350178 >>12350198 >>12350204 >>12350251 >>12350732 >>12350938 >>12351419 >>12351596 >>12354526 >>12354705 >>12354741 >>12355031 >>12355043

how many elements from the set $A=\{0.49, 0.499, 0.4999, ...\}$ are equal to 0.5?

Anonymous

Anonymous Mon 16 Nov 2020 16:42:49 No.12350178 Report

Quoted By: >>12350186

>>12350175
None

Anonymous

Anonymous Mon 16 Nov 2020 16:46:12 No.12350186 Report

Quoted By: >>12354551

>>12350178
0.4999...=0.5

Anonymous

Anonymous Mon 16 Nov 2020 16:50:22 No.12350198 Report

Quoted By: >>12350218 >>12350737

>>12350175
Am I a brainlet or is it obviously 1?

Anonymous

Anonymous Mon 16 Nov 2020 16:52:22 No.12350204 Report

Quoted By: >>12350243 >>12351419

>>12350175
none
however the supremum of this set, coloquially known as 0.4999..., is equal to 0.5

Anonymous

Anonymous Mon 16 Nov 2020 16:58:28 No.12350218 Report

Quoted By: >>12350737

>>12350198
The answer is either 1 or none. If it is indeed 1, then it receives the notation ~=

Anonymous

Anonymous Mon 16 Nov 2020 17:01:01 No.12350221 Report

Quoted By:

All of them. Unless you use floating point, then only after the ninth entry. Further down if double precision, obviously

Anonymous

Anonymous Mon 16 Nov 2020 17:02:24 No.12350223 Report

Quoted By:

only the biggest one

Anonymous

Anonymous Mon 16 Nov 2020 17:07:31 No.12350243 Report

Quoted By: >>12350246 >>12350365 >>12350625

>>12350204
there is no largest element in the set anon

Anonymous

Anonymous Mon 16 Nov 2020 17:08:14 No.12350246 Report

Quoted By:

>>12350243
>supremum
Yes there is, I saw it, you didn't scroll to the right far enough. It's .5.

Anonymous

Anonymous Mon 16 Nov 2020 17:11:09 No.12350251 Report

Quoted By: >>12350279

>>12350175
The set you describe has infinitely many elements. The largest element of the set which is also the last element is equal to 5. Sets of the form you describe have an ultimate element but no penultimate element.

Anonymous

Anonymous Mon 16 Nov 2020 17:20:37 No.12350279 Report

Quoted By: >>12350343

>>12350251
>it has infinitely many elements
>the largest element
>the last element

Anonymous

Anonymous Mon 16 Nov 2020 17:36:12 No.12350343 Report

Quoted By: >>12350468

>>12350279
yes
consider {...,-2,-1,0,1}

Anonymous

Anonymous Mon 16 Nov 2020 17:41:28 No.12350365 Report

Quoted By: >>12351419

>>12350243
the supremum doesn't have to be in the set, it's the least upper bound

Anonymous

Anonymous Mon 16 Nov 2020 18:12:39 No.12350468 Report

Quoted By: >>12350682

>>12350343
what about it?

Anonymous

Anonymous Mon 16 Nov 2020 18:53:10 No.12350625 Report

Quoted By: >>12350673

>>12350243
never said there is

Anonymous

Anonymous Mon 16 Nov 2020 19:06:09 No.12350673 Report

Quoted By: >>12350712

>>12350625
every 0.49... is in the set

Anonymous

Anonymous Mon 16 Nov 2020 19:09:52 No.12350682 Report

Quoted By: >>12354569

>>12350468
consider it

Anonymous

Anonymous Mon 16 Nov 2020 19:22:41 No.12350712 Report

Quoted By:

>>12350673
notation implies that only decimals with finite number of 9's are in the set. every sane person would write $A = \{ 0.49, 0.499,0.4999,\dots,0.4999\dots\}$ if they wanted to include 0.4999...

Anonymous

Anonymous Mon 16 Nov 2020 19:26:52 No.12350732 Report

Quoted By:

>>12350175
I think that 0.5 is the least upper bound of the set and it does not belong to the set. This because it is always possible to get a $a \in A:0.5-\epsilon<a<0.5$ for any given $\epsilon>0$ , but no element of A is greater or equal 0.5.

Anonymous

Anonymous Mon 16 Nov 2020 19:28:20 No.12350737 Report

Quoted By:

>>12350218
>>12350198
Yes

Anonymous

Anonymous Mon 16 Nov 2020 20:33:41 No.12350938 Report

Quoted By: >>12350941

>>12350175
Depends on how you define "equal to". If it means "same number as" than none, if it means "less than" then infinitely many

Anonymous

Anonymous Mon 16 Nov 2020 20:34:48 No.12350941 Report

Quoted By: >>12350992

>>12350938
>depends on whether "=" means "=" or "<"

Anonymous

Anonymous Mon 16 Nov 2020 20:47:52 No.12350992 Report

Quoted By:

>>12350941
symbols have multiple meanings, for example "=" can mean "equal to" or "parallel to"

Anonymous

Anonymous Mon 16 Nov 2020 22:42:28 No.12351419 Report

Quoted By:

>>12350175
These anons are correct:

>>12350204
>>12350365

El Arcón

El Arcón Mon 16 Nov 2020 23:01:55 No.12351505 Report

Quoted By: >>12351624

$<br /> 0.999...\equiv\lim\limits_{n\to\infty}\sum_{k=1}^n\frac{9}{10^k}=1<br />$
This follows unambiguously from the Cauchy $\varepsilon\!-\!\delta$ definition of the limit. But what about
$<br /> \lim\limits_{n\to(\widehat\infty-1)}\sum_{k=1}^n\frac{9}{10^k}\stackrel{?}{=}1<br />$
If the second one is also equal to one, then infinite elements of the OP sequence are equal to 0.5.

Anonymous

Anonymous Mon 16 Nov 2020 23:23:50 No.12351596 Report

Quoted By:

>>12350175
All of them because I rounded up

Anonymous

Anonymous Mon 16 Nov 2020 23:29:27 No.12351624 Report

Quoted By:

>>12351505
some pretty nonstandard anal going on here my guy

Anonymous

Anonymous Tue 17 Nov 2020 15:16:40 No.12354526 Report

Quoted By:

>>12350175
>>12345678

Anonymous

Anonymous Tue 17 Nov 2020 15:22:15 No.12354551 Report

Quoted By:

>>12350186
it's not there tho.

Anonymous

Anonymous Tue 17 Nov 2020 15:24:04 No.12354560 Report

Quoted By:

None. Each element only has finitely many 9s, so none of them are equal 5.
What a meme board /sci/ is. Holy fuck

Anonymous

Anonymous Tue 17 Nov 2020 15:27:39 No.12354569 Report

Quoted By:

>>12350682
Nice comeback anon

Anonymous

Anonymous Tue 17 Nov 2020 16:07:56 No.12354705 Report

Quoted By:

>>12350175
None.
But, sup(A) = 5

Anonymous

Anonymous Tue 17 Nov 2020 16:18:25 No.12354741 Report

Quoted By:

>>12350175
It's an open set with supremum 0.5, so none.

Anonymous

Anonymous Tue 17 Nov 2020 17:26:37 No.12355031 Report

Quoted By:

>>12350175
None, for the same reason infinity isn't an element of the naturals.

Anonymous

Anonymous Tue 17 Nov 2020 17:28:49 No.12355043 Report

Quoted By:

>>12350175
3, now answer mine >>12355002

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