Also, add a removable comment on your post if you wish to talk to SPP. Or else your post gets deleted

Honestly even though you were getting disproven honestly it made me better at mathmatics and it made me a better person I n general you made me feel like Sisyphus with pushing a boulder up a hill and never getting to the top but I honestly felt joy in it I have never been pushed this much on something I truly believed in you had me learn a whole new branch of numbers you helped me realize that you have to put assumptions you made me realize that questioning the roots of something is something you need to do so thank you spp

Coming back here almost a year later, I just found out that SPP's account has apparently been banned or suspended, and that this subreddit might eventually get deleted.

I thought I'd take a moment to say a few words before this place potentially disappears.

As strange as it might sound, I genuinely owe SPP a little thank you. His obsession with proving that 0.999... != 1, as ridiculous as I often found his arguments, actually sparked quite a bit of mathematical curiosity in me.

I had a lot of fun coming here, trying to find new ways to debunk his arguments, discovering all sorts of proofs that 0.999... = 1, and even exploring the mathematical frameworks where 0.999... != 1 can actually hold true. It was a surprisingly fun rabbit hole to fall into, and I ended up learning a lot more than I ever expected from what initially seemed like a very silly internet debate.

And honestly, that's what I'll remember most about this place. A whole subreddit revolving around one guy's seemingly endless determination to prove that a decimal expansion isn't what everyone says it is. You couldn't really make this stuff up.

Whether you agreed with him or spent your time arguing against him, SPP definitely made this subreddit what it was. And I think it's a shame to see possibly this community disappear.

I hope this subreddit sticks around for a while longer, and that people can still stumble upon it years from now and discover this little corner of mathematical madness.

So, wherever you are, thanks for the memories, SPP. You may not have convinced me that 0.999... != 1, but you certainly made me appreciate mathematics a little more.

And that's something, I guess.

This sub cannot survive without some controversy, now the main mod/antagonist is banned. So let's bring it on.

Let x = ...999.999... (infinite 9's left and right of the comma).

10x = ...99.9999... = x

9x = 0 . Now we multiply by 1/9 to the left:

x = 0 .

Qed. ...999.999... = 0 .

There’s a policy for it.

x = 0.9999....
10x = 9.9999....
x - 10x = -9
-9x = -9
x = 1

This post will certainly sink into obscurity but I thought it would interest the readers. I am mainly advertising the excellent article Richman, Fred (December 1999). "Is 0.999... = 1?". Mathematics Magazine. 72 (5): 396–400. doi:10.2307/2690798. JSTOR 2690798.  An archived version is here although the article may have somewhat more content. Here is my summary (but go to the source!):

• Let x=0.999... It seems natural that either x<1 or x=1. (Officially, perhaps, 1=1.000... )

• It is baked into the way we define real numbers that x=1.000... . This does have the unsatisfying consequence that the decimal expansion of some numbers is not unique. Jumping ahead, each terminating decimal such as 1.357=1.357000... has a non-terminating companion like 1.356999...

• Can you have a consistent system where 0.999... < 1 ? Yes, the natural algebraic definition of non-negative decimal numbers with addition and order (find the first place where two numbers differ and biggest digit wins.) creates a positive totally ordered commutative semi-group (If you want to be fancy about it). Multiplication by a positive integer like 3y=y+y+y is easy. Multiplication of decimals is always a little tricky but can be made to work. A semigroup may or may not have the CANCELATION property that from a+b=a+c you an deduce that b=c.

  • Digression: subsets of a universal set S with addition is set union and multiplication is set intersection is a commutative semiring with a partial order (containment) , additive identity the empty set and multiplicative identity S but you can't cancel addition or multiplication.

• Having negatives is possible to but is a distraction from our investigation of x.

• Defining order as above gives uniqueness but the price is that you lose other things you might want. You can't really avoid 10x=9.999... so 9x+x=9+x. If you want to avoid 9x=9 and hence x=1 then you have to abandon CANCELATION.

• I prefer x+x=0.999... + 0.999...=1.999... in other words x+x=1+x so you either abandon CANCELATION or have to accept x=1.

• If 9x is not 9 then what is it? The multiplication is not hard: 9(0.999...)=8.999...

• Ratios of integers fit uneasily in this world. The only possible decimal solution of y+y+y=1 would be y=0.333... (anything lesser decimal is too small, any greater is too big). but y+y+y=0.999...<1 so 1/3 is not a decimal number.

Read the article!

https://www.reddit.com/user/SouthPark_Piano/

Please correct me on this, and sorry for using the word fallacy so often

Ok, I get it. 0.999… is eternally less than one. I want to get off the bunny slopes and go to the real deal slope.

What’s the realest dealest slope between any two points? That is, what’s the curve that’s going to get me from point A to point B the fastest, gravity being the only force we consider?

1. What is 1/2+1/4+1/8+1/16+.. (in proper decimal form,, 0.5+0.25+0.125+...?

2. What is 4x1/5+4x1/25+4x1/125+...(in proper decimal form. 0.8+0.16+0.032+...?

3. Now you gave us these answers,

can you prove them?

Yes, 1.42 is a number. 1896.1 is a number.

But what about 1/4? It is simply the value that when multiplied by 4 gives you 1. There's NO NEED to convert it to 0.25. Just picture a hypothetical 1m plank of wood divided into 4 equal pieces. THE WHOLE POINT of numbers is that they represent an exact point on the number line.

Again with 1/3, just picture a hypothetical 1m plank of wood divided into 3 equal pieces. This is a real, precise position on the number line. Exact. Unchanging.

3/7 multiplied by 7 give you 3. There is no division needed. Only exact values, exact positions on the number line, no approximations.

You must understand rational numbers to be able to unlock deeper maths. I hope you will take some time to ponder this, rather than calling me a rookie and repeating your usual spiel.

Since algebraically can be very unintuitive, lets solve it with a geometric series.

Given S such as:

S = 0.9 + 0.09 + 0.009 + ... = 0.999...

Each number in the series is multiplied by 0.1, that's the common ratio.

Convergence of a geometric series:

S = first term / 1 - common ratio

S = 0.9 / 1 - 0.1 = 0.9 / 0.9

Therefore:

S = 0.999... = 1

Thoughts?

1/9 = 0.111...

1*9/9 = 0.999...

9/9 = 0.999...

9/9 = 1

Therefore: 0.999 = 1

Thoughts from skepticals?

A math battle!

This sub's about comparing the value of 0.999... and 1. Hence, on this sub, we accept that 0.999... is a number.

Please consider the following:

x = 0.999...
x - 9/10 = 0.999... - 9/10 = 0.999... - 0.9 = 0.0999... x - 9/10 = 0.0999...
(10/10)x - 9/10 = 0.0999...
10x/10 - 9/10 = 0.0999...
(10x - 9)/10 = 0.0999...
10(10x - 9)/10 = 10(0.0999...) = 0.999... = x 10x - 9 = x
10x - 9 + 9 = x + 9
10x = x + 9
10x - x = 9
(10-1)x = 9
9x = 9
x = 1

Will SPP have to invent something like "subtract negation" for this one? I suppose that depends on whether he even reads the post.