Anonymous at Sun, 16 Feb 2025 02:42:31 UTC No. 16587506

It's actually .FFF...

Anonymous at Sun, 16 Feb 2025 02:43:56 UTC No. 16587508

Anonymous at Sun, 16 Feb 2025 03:15:27 UTC No. 16587536

Imagine you have a pizza. You divided pizza in 3 slices. You ate all 3 slices. How many pizzas did you eat?

Anonymous at Sun, 16 Feb 2025 04:17:25 UTC No. 16587570

>>16587536
>many
3

Anonymous at Sun, 16 Feb 2025 05:01:42 UTC No. 16587587

>>16587494
What do 1 and 3 mean? Are they taken as reals here or as rationals?

Anonymous at Sun, 16 Feb 2025 05:03:08 UTC No. 16587588

>>16587494
.99999.... = 3/3 = 1
This feels like a contradiction.

Anonymous at Sun, 16 Feb 2025 05:04:05 UTC No. 16587589

>>16587588
>.99999.... = 3/3
That's not true tho

Anonymous at Sun, 16 Feb 2025 10:12:28 UTC No. 16587728

>>16587589
[eqn]\frac{1}{3}=0.3...[/eqn]
[eqn]3\cdot\frac{1}{3}=3\cdot0.3...[/eqn]
[eqn]\frac{3}{3}=0.9...[/eqn]
[eqn]1=0.9...[/eqn]
seethe

Anonymous at Sun, 16 Feb 2025 10:27:54 UTC No. 16587745

>>16587728
>3 * 0.333... = 0.999...
Proofs? Or did a jewtuber tell you and you believed him?

Anonymous at Sun, 16 Feb 2025 11:20:07 UTC No. 16587769

0.3_ approaches 1, it isn't actually 1.

Anonymous at Sun, 16 Feb 2025 11:26:39 UTC No. 16587773

>>16587769
number cannot approach anything. number is static.

Barkon !8v8vr3ErDk at Sun, 16 Feb 2025 11:27:31 UTC No. 16587774

It's a wacademic con. It helps make the fake unfair world go round.

Barkon !8v8vr3ErDk at Sun, 16 Feb 2025 11:28:32 UTC No. 16587775

>>16587769
Approach a rope.

Barkon !8v8vr3ErDk at Sun, 16 Feb 2025 11:29:45 UTC No. 16587777

Such commotion to depict a third.

Anonymous at Sun, 16 Feb 2025 12:14:59 UTC No. 16587803

>>16587494
>why is 3/3=1 and not 0.99999 forever?
the source of this incurable confusion is that it's both
>>16587588
>This feels like a contradiction.
well it's not

Anonymous at Sun, 16 Feb 2025 12:20:05 UTC No. 16587808

>>16587536
The tool I used to divide the pizza with will have caught some miniscule amount of the pizza. So I ate 0.9999999999 pizzas.

Anonymous at Sun, 16 Feb 2025 12:20:23 UTC No. 16587809

>>16587494
Why do we have a thread like this every single day of the week and people debating the point as if it was worth discussing?

Barkon !8v8vr3ErDk at Sun, 16 Feb 2025 12:20:58 UTC No. 16587810

Time to grow up

Anonymous at Sun, 16 Feb 2025 12:28:39 UTC No. 16587818

>>16587809
this and what exactly is the value of "6/2(2+1)" are the two great unanswered questions of modern mathematics

Anonymous at Sun, 16 Feb 2025 12:37:47 UTC No. 16587825

>>16587809
We will keep btfoing them until .999... = 1 subhumans learn their place

Barkon !8v8vr3ErDk at Sun, 16 Feb 2025 12:57:49 UTC No. 16587835

>>16587825
Fite me for it bro

Anonymous at Sun, 16 Feb 2025 14:33:11 UTC No. 16587917

>So, if that's the case, why is 3/3=1
Because if you cut a pizza into three pieces of equal size and give them all to Bob, you have given one whole pizza

Anonymous at Sun, 16 Feb 2025 14:41:44 UTC No. 16587927

>>16587917
Wrong. There's still crumbs on the cutting board.

Anonymous at Sun, 16 Feb 2025 19:37:27 UTC No. 16588329

>>16587494
>why is 3/3=1 and not 0.99999 forever?
That's a nonsense question, those mean the same thing.

Anonymous at Sun, 16 Feb 2025 23:45:47 UTC No. 16588575

>>16587494
0.333333333+0.666666666666=1

Anonymous at Mon, 17 Feb 2025 00:33:43 UTC No. 16588602

>>16587494
.999 forever and 1 are the same number. There is no last little bit because there is bo number higher than .99 forever and less than 1, because they are the same number

Anonymous at Mon, 17 Feb 2025 02:12:19 UTC No. 16588656

>>16587494
We of the ONE TRUE FINITE FAITH have resolved this matter. By talking to GOD!
Here's what GOD said.
"Look, just tell those assholes to fuck off with this bullshit, the simple fact is you can NOT divide anything by another number when it gives an infinity repeating decimal. It just cant happen, okay? So dont do it, Just do something else instead, watch TV, help an old lady across the road, club a baby seal over the head, pick your nose, suck a dick, whatever, I dont care just dont do this infinity bullshit"
Then GOD said...
"Infinity is an affront to the natural order of things, and to me personally. If you had any sense you would burn at the stake anyone who even mentions the word. Now piss off and hunt down some Heretics."

We of the ONE TRUE FINITE FAITH are the chosen people. Also. Fuck off you assholes.
Amen.

Anonymous at Mon, 17 Feb 2025 08:29:46 UTC No. 16588962

Python 3.12.8 (main, Jan 18 2025, 15:12:31) [GCC 14.2.1 20241221] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> 0.333333333333333333333333333333333+0.6666666666666666666666666666
1.0

Anonymous at Mon, 17 Feb 2025 08:40:20 UTC No. 16588971

>>16587494
>why is 3/3=1 and not 0.99999 forever?
0.999999... literally means 1, retard.

Anonymous at Mon, 17 Feb 2025 09:12:05 UTC No. 16589004

No, open interval from 0 to 1 ends at one.
Closed interval from 0 to 1 ends at 0.999999

It's this strange situation, that those are two real numbers in between which you can't fit another number, like next to each other on real axis, but not same point.

Anonymous at Mon, 17 Feb 2025 09:31:35 UTC No. 16589014

>>16589004
Cope.

Anonymous at Mon, 17 Feb 2025 09:37:37 UTC No. 16589019

>>16589014
Your font sucks.

Anonymous at Mon, 17 Feb 2025 09:39:07 UTC No. 16589020

>>16589019
font discussions belong on >>>/lgbt/

Anonymous at Mon, 17 Feb 2025 09:49:31 UTC No. 16589026

>>16589020
I don't know what's going on that board, I'm not such fag as you.

Anyway, it seems like you can't do maths.

Anonymous at Mon, 17 Feb 2025 09:52:35 UTC No. 16589028

>>16589026
math is made up, I can define anything to be true, seethe

Anonymous at Mon, 17 Feb 2025 09:55:54 UTC No. 16589032

>>16589014
Best you can do in Maths is to donate your organs to some sick mathematicans after you kill yourself.

Anonymous at Mon, 17 Feb 2025 21:09:52 UTC No. 16589543

This thread is now about signed-digit notation and doing arithmetic with infinite decimals.
[math]1 = 01 = 1\overline{9} = 1.0 = 1.\overparen{0} = 0.\overparen{9} = 2.\overparen{ \overline{9} } = 1\overline{ 998 }.\overparen{ \overline{9} }[/math]

A line over a digit indicates a negative digit.
An arc over a group of digits means that group of digits is infinitely repeated.

Terminating decimals reperesent the sum of each digit multiplied by the place value of its position. For example:
[math]4\overline{ 35 }.6\overline{ 7 }[/math] = 4 hundreds + (-3) tens + (-5) ones + 6 tenths + (-7) hundredths

One use of signed digits is to simplify arithmetic calculations. For example, the trick of multiplying by 9 by multiplying by 10 and subtracting is exactly the same as rewriting 9 as [math]1\overline{1}[/math] and multiplying with the standard algorithm.

Infinite decimals represent the value whose distance from any finite decimal that we get by ending the infinite decimal at some position is at most the place value of that position, no matter where we end the decimal. For example:
The distance between [math]2.\overparen{ \overline{9} }[/math] and 2 is at most one.
The distance between [math]2.\overparen{ \overline{9} }[/math] and [math]2.\overline{9}[/math] is at most one tenth.
The distance between [math]2.\overparen{ \overline{9} }[/math] and [math]2.\overline{99}[/math] is at most one hundredth.

Anonymous at Mon, 17 Feb 2025 21:10:53 UTC No. 16589544

Each of these statements about the infinite decimal can be visualized as a segment of the number line which the number must lie in. These segments include their endpoints. We call segments of the number line which may or may not include their endpoints intervals, and we call them closed intervals if they include their endpoints. We will write a closed interval by writing the numbers at the endpoints of the interval in order with a comma between them and enclosed by square brackets.
For example:
[1, 3] means the numbers between 1 and 3 inclusive.
And we can write the intervals which [math]2.\overparen{ \overline{9} }[/math] must lie in as
[1, 3]
[math][1.0, 2.\overline{8}][/math]
[math][1.00, 2.\overline{98}][/math]
and so on.
Without using negative digits, the same intervals can be written as
[1, 3]
[1.0, 1.2]
[1.00, 1.02]
and so on.
If you draw these intervals out on the number line, you can see that they shrink towards 1.

So an infinite decimal specifies a number by giving an infinite list of intervals which include the number. Each interval is a part of the previous interval in the list; we say the intervals are nested. We can also see that the size of these intervals eventually becomes smaller than any given place value. For example, in the intervals of [math]2.\overparen{ \overline{9} }[/math], the first interval which is smaller than a thousandth is the interval of numbers at most [math]\frac{1}{10 000}[/math] from [math]2.\overline{9999}[/math], which is [1.0000, 1.0002] and has a size of [math]\frac{2}{10 000}[/math]. We call a sequence of nested closed intervals satisfying this property of eventually becoming arbitrarily small a nest. Every infinite decimal describes a number using a nest it must be in, but nests need not be obtained directly from an infinite decimal.

Anonymous at Mon, 17 Feb 2025 21:11:53 UTC No. 16589546

We assume that the distance between two different numbers on the number line must be at least one of some place value. For example, 0.9 and 1 are one tenth apart, 0.3 and [math]\frac{1}{3}[/math] are more than three hundredths apart, and 0.999 and 1 are one thousandth apart. Under this assumption, it is impossible for a nest to contain more than one number, since we can find a place value small enough to fit between the numbers, and the nest must contain an interval smaller than that place value. We will also assume that every nest contains a number. So every nest and every infinite decimal denotes exactly one point on the number line.

If we know that one number is in one closed interval and a second number is in a second closed interval, we can find closed intervals which must contain their sum, difference, product, and assuming the second interval doesn't include zero, their quotient. This is called interval arithmetic. Let's do an example. Suppose the number x is in [3, 5] and the number y is in [1, 2]. What can we say about the difference x - y? The smallest x - y can be is if x = 3 and y = 2; in that case x - y = 1. The largest x - y can be is if x = 5 and y = 1; in that case x - y = 4. We conclude that x - y is in the interval [1, 4] and we write
[3, 5] - [1, 2] = [1, 4].

Given two nests, we can use interval arithmetic to find nests containing the sum, difference, product, and, under the condition the second nest does not contain zero, the quotient of the numbers in the nests.
As an example, let's find the first few intervals of a nest containing [math]0.\overparen{3} + 0.\overparen{6}[/math].
[-1, 1] + [-1, 1] = [-2, 2]
[0.2, 0.4] + [0.5, 0.7] = [0.7, 1.1]
[0.32, 0.34] + [0.65, 0.67] = [0.97, 1.01]
[0.332, 0.334] + [0.665, 0.667] = [0.997, 1.001]

Anonymous at Mon, 17 Feb 2025 21:12:54 UTC No. 16589547

We can also turn nests back into infinite decimals.
[0.7, 1.1] is part of [0, 2], so we can choose a decimal beginning with 1.
[0.97, 1.01] is part of [0.9, 1.1], so we can choose a decimal beginning with 1.0.
[0.997, 1.001] is part of [0.99, 1.01], so we can choose a decimal beginning with 1.00.
This process continues to add zeros to the decimal forever, so [math]0.\overparen{3} + 0.\overparen{6} = 1.\overparen{0}[/math].

Anonymous at Mon, 17 Feb 2025 23:35:26 UTC No. 16589685

>>16587728
0.999... + 0.999... + 0.999... = 3 × 0.999...
= 2.997...
≈ 3
This series of equations seems to show that:
0.999... + 0.999... + 0.999... ≠ 3
However, since 0.999... converges to 1, we can substitute:
1 + 1 + 1 = 3
This play on numbers highlights the importance of understanding the concept of convergence in mathematics.

Anonymous at Mon, 17 Feb 2025 23:43:35 UTC No. 16589688

>we're apparently still making the pretend infinitesimals are real post
Damn, you retards must really love infinity if you're gonna keep dividing by it.

Anonymous at Tue, 18 Feb 2025 13:30:06 UTC No. 16590162

>>16589688
& here i whas thinking ultrafilters where merely mahtematical, turns out that people can be affcted by them as well

Anonymous at Fri, 21 Feb 2025 03:31:56 UTC No. 16594390

>>16589004
1, you mixed up open and closed intervals. Open intervals don't include the ends. Closed intervals include the ends.
2.Open sets don't have an end. The defining property of an open set in a metric space is that no matter how close you get to the edge, you can always get a little closer and stay inside the open set.

3. There are number system that works like how you're saying. It just isn't the real numbers. You might enjoy reading about "hyperreal numbers", and "dual numbers".

Anonymous at Fri, 21 Feb 2025 06:12:24 UTC No. 16594473

>>16594390
Yea, I mixed up, it's more than 10years since I've heard about intervals in school. Memory decay.

Anonymous at Fri, 21 Feb 2025 07:28:48 UTC No. 16594513

>>16587494
you broke math. congrats.

Anonymous at Fri, 21 Feb 2025 08:40:30 UTC No. 16594561

>>16587494
Someone who doesn't believe 0.999...=1 also doesn't believe 0.333...=1/3, though.

Anonymous at Fri, 21 Feb 2025 11:45:48 UTC No. 16594683

>>16587494
OP everyone here is gaslighting you, but your intuition is actually correct. 0.9999 is NOT equal to 1 and 0.3333 is NOT equal to 1/3. modern math only treats these numbers as such because it finds that the sum of the infinite geometric series of 9/10 + 9/100 + 9/1000... is 1. HOWEVER, the assumption that infinity itself exists is not proven. It's just an axiom that is taken for granted by ZF theory

Anonymous at Fri, 21 Feb 2025 13:08:43 UTC No. 16594741

>>16594683
how do you define 0.999... and 0.333... that you claim these numbers are distinct from 1 and 1/3?

Anonymous at Fri, 21 Feb 2025 13:38:40 UTC No. 16594767

>>16594741
>how do you define 0.999... and 0.333... that you claim these numbers are distinct from 1 and 1/3?
Why does he need to define them? He doesn't believe they are numbers. He rejects the notion of convergence. You can define the notion of convergence coherently within some self-contained framework and claim that it is, therefore, valid. But he can say he rejects your framework, because no framework lives in a vacuum, and your framework contradicts his notion of infinity.

Anonymous at Fri, 21 Feb 2025 13:58:08 UTC No. 16594794

>>16594390
Don't you want to spoonfeed me and tell me some good book?

Anonymous at Fri, 21 Feb 2025 15:16:45 UTC No. 16594901

>>16594767
>He doesn't believe they are numbers
why do you think so?

Anonymous at Fri, 21 Feb 2025 17:29:32 UTC No. 16595109

>>16594901
He literally says it.

Anonymous at Fri, 21 Feb 2025 18:03:14 UTC No. 16595140

>>16595109
He literally doesn't.

Anonymous at Fri, 21 Feb 2025 18:30:10 UTC No. 16595169

>>16589685
A single number can't converge.
The series 9*Sum[10^-i,{i,1,inf}] = 0.9 + 0.09 + 0.009 + .... = 0.999...
Using the calc 1 you surely know, since you're so obviously smart and don't even understand limits, you can easily calculate the final result.
For a geometric series, the sum is exactly equal to a/1-r assuming 0 < r < 1.
a is the initial value, in this case 0.9. r is the ratio between any two values, in this case 0.1
0.9/(1-0.1) = 0.9/0.9 = 1

Anonymous at Fri, 21 Feb 2025 18:41:25 UTC No. 16595186

>>16595140
It's ok, I'm used to the fact that almost every single one of you has an IQ of 80 and a raging, delusional mental illness.

Anonymous at Fri, 21 Feb 2025 19:43:47 UTC No. 16595315

>>16595186
>He doesn't believe they are numbers.
correct. infinities should have no place in math or physics. they are simply conveniences until they stop yielding useful results

Anonymous at Fri, 21 Feb 2025 22:06:52 UTC No. 16595522

>>16595315
How can you even build a bridge without acknowledging conveniences?

Anonymous at Fri, 21 Feb 2025 23:59:29 UTC No. 16595715

They say 0.99999 infinte is the same as 1, written in different form.

I've never believed it, but it doesn't matter what I do believe it seems.

Anonymous at Sat, 22 Feb 2025 00:01:40 UTC No. 16595722

>>16595315
It's like "there are bigger infinites than others, you can prove it with the diagonal proof of cantor"

except you assumed you can finish a infinite in the first place, dumbass.

Anonymous at Sat, 22 Feb 2025 00:16:47 UTC No. 16595748

>>16595722
What the fuck do you mean "finished an infinite"? Are all mathematics deniers retarded or does /sci/ just attract particularly retarded contrarians?

Anonymous at Sat, 22 Feb 2025 01:45:40 UTC No. 16595841

>>16595748
they don't know what convergence is lol. it's impossible to discuss anything among these schoolchildren

Anonymous at Sat, 22 Feb 2025 04:19:41 UTC No. 16595923

>>16587494
Keav

Anonymous at Sat, 22 Feb 2025 08:24:39 UTC No. 16596024

>>16594794
If you haven't taken courses on (standard) real analysis, abstract algebra, and topology, I think the best book for you is this:

https://people.math.wisc.edu/%7Ehkeisler/calc.html

Goes into how to use/think about hyperreal numbers without getting mired in the abstract formalisms (though it does present a construction of the hyperreals in an appendix, if you want).

Anonymous at Sat, 22 Feb 2025 08:26:27 UTC No. 16596025

>>16595315
My brother in Christ, I have yet to see the day when infinities stopped yielding useful results. I'll let you know when that day comes.

Anonymous at Sat, 22 Feb 2025 10:02:54 UTC No. 16596095

>>16595748
Cantor proof assumes a complete correlation of natural numbers to all fractional numbers inbetween 0.0 and 1.0
I'm not denying maths, but that proof always sound absolutely disgusting to ever be taken seriously

Anonymous at Sat, 22 Feb 2025 10:15:05 UTC No. 16596117

>>16596024
I watched some videos about abstract algebra, my biggest problem isn't understanding concepts, but remembering notation.

Anonymous at Sat, 22 Feb 2025 11:40:14 UTC No. 16596230

>>16596095
I'm going to guess by "Correlation" you mean a bijection. As in we give each rational between 0 and 1 a label from the set {1,2,3,4,...} Here is your bijection:

Make a 2d grid of points, Which represents [math] \mathbb{N} \prod \mathbb{N} [/math]. Partition this grid into cross diagonal, sets, i.e. {[math] (k, n-k + 1) | k = 1, ... , n[/math]}.

Start at the point (1,1) and give it the label 1. Move to the second diagonal, and label each point new point you come across with the next natural number. BUT if you come across a scalar multiple of a previously labeled point, you skip it. Rinse and repeat.

Anonymous at Sat, 22 Feb 2025 11:42:13 UTC No. 16596232

>>16596230
Oops sorry guys, [math] \mathbb{N} \prod \mathbb{N} [/math] should have been [math] \mathbb{N} \times \mathbb{N} [/math]

Anonymous at Sat, 22 Feb 2025 11:44:02 UTC No. 16596234

>>16596117
I'd say the level of understanding of abstract algebra you need is more than having watched some videos. I am a firm believer that real learning in math simply cannot live without doing homework, completing exercises, doing proofs. Videos are a good start, but watching is no substitute for doing.

Anonymous at Sat, 22 Feb 2025 14:58:40 UTC No. 16596405

>>16587773
>number cannot approach anything. number is static.

If 0.1[base 10] is "static" for you,
Then not true if you convert between bases in decimals.

Try to convert 0.1 = 1*10^(-1) [base 10] in [base 2] without infinite 0 and 1 decimals...

Reminder :

0.0001[base 2] = 0.0625
0.001[base 2] = 0.125
0.01[base 2] = 0.25
0.1[base 2] = 0.5
1[base 2] = 1
10[base 2] = 2
100[base 2] = 4
1000[base 2] = 8
...

Now try to convert 0.1[base 10] in [base 2]...

Anonymous at Sat, 22 Feb 2025 15:02:30 UTC No. 16596406

>>16587494
Every single one of you is extremely retarded

Anonymous at Sat, 22 Feb 2025 16:48:01 UTC No. 16596492

>>16587745
It's obvious

Anonymous at Sat, 22 Feb 2025 18:51:04 UTC No. 16596595

>>16596405
I don't think you and that poster disagree. 0.1 is doesn't change (is "static") no matter what base you write it in... ?

Anonymous at Sat, 22 Feb 2025 19:36:41 UTC No. 16596650

>>16596405
How are you so retarded you don't understand convergence but think you have some insight into different bases

Anonymous at Sat, 22 Feb 2025 20:25:27 UTC No. 16596711

>>16596650
>you don't understand convergence
That's the point of this post :
>>16596405

You need to use convergence to define some numbers with decimals if you convert them between different bases.

If not, you're as dumb as an electronic calculator.

Anonymous at Sat, 22 Feb 2025 20:45:22 UTC No. 16596731

>>16596711
I'm not part of this discussion and I assume you're all retarded.

That said, it's interesting to imagine a calculator that would give the closest plausible numerator and denominator instead of the decimal result. Such a calculator would also be retarded. Make of that what you will.

Anonymous at Sun, 23 Feb 2025 00:25:53 UTC No. 16596930

>>16587494

chat its in 9th grade mathematics, still I'll tryna explain in ma why
Math:
Let x = 0.99999…
10x = 9.99999…
10x — x = 9.00000…
10x — x = 9
9x = 9
x = 1

0.999... means its goes on for infinity. Unless you're a dick you know that infinity can't be comprehended, so the gap between 1 and 0.999... becomes so so small that it's fine to get ignored

Anonymous at Sun, 23 Feb 2025 02:21:05 UTC No. 16597008

>>16596711
Some rational numbers can't be represented in a finite number of digits in certain bases.
A single number does not change nor converge, no matter what base you represent it in.
Convergence is "eventually reaching a point," and a single point never "reaches" a point, it IS the point.

Anonymous at Sun, 23 Feb 2025 04:42:17 UTC No. 16597071

you can't divide things
only distribute

Anonymous at Sun, 23 Feb 2025 05:13:17 UTC No. 16597090

>>16596405
>Now try to convert 0.1[base 10] in [base 2]...
https://www.rapidtables.com/convert/number/base-converter.html

Anonymous at Sun, 23 Feb 2025 11:28:37 UTC No. 16597232

>>16596930
>becomes so so small that it's fine to get ignored
actualy if we work in th eextened real numbers we finaly get a lable for the position of the 1 that finitist bemoan the existance of, but it turns out that that same lable turns that 1 into a 0, and so while existent it's rendered moot, sadly many finitist don't even know how positional notation works, so that is that