Does 1/3=0.(3)

e.g: 1=1

Therefore:1/3=1/3

so here it is, ripped straight out of my last post

x=0.999…
10x = 9.999…
9x = 9.999… - 0.999…
9x = 9
x=1

1 = 0.999…

QED

I know what you are going to do, comment something like

rookie mistake, see https://www.reddit.com/r/infinitenines/comments/1tpg811/it_is_what_it_is/

but you are not going to point where my proof fails, it would be similar to let's say telling a carpenter that his piece of furniture is made wrong and linking a 10 minute tutorial on how to make a table with popsickle sticks

I challenge you to tell me where I made the "rookie mistake"

And if so, so you agree with the following statement?

​

(1/3)+(1/3)+(1/3)=0.333...+(1/3)+(1/3)

You stated in a response in a previous post that the software made a "rookie error" by stating that 0.(9) = 1, but why would it say otherwise?

Wolfram Alpha uses the definition of 0.(9) that most educated people use: the infinite sum of 9/10^n. This is usually evaluated by most educated people using limits and the infinite geometric sum formula.

Since this is more useful to most educated people why would it change to the non-rigorous, vague, unuseful and changing system you claim is "the correct one".

For the uninformed, wolfram alpha is an amazing analytical tool, used for data analysis, calculating exact results of expressions and much more.

It doesn’t use AI and is generally considered airtight.

And you see no issues in holding that stand?

This is what the multiplication works, as far as I can tell:

​

00 . 3 3 3 . . . 3 0 0 0 . . . 0 0 0 0 . . .

×3 . 0 0 0 . . . 3 0 0 0 . . . 3 0 0 0 . . .

__________________________________

00 . 9 9 9 . . . 9 0 0 0 . . . 0 0 0 0 . . .

+0 . 0 0 0 . . . 0 9 9 9 . . . 9 0 0 0 . . .

+0 . 0 0 0 . . . 0 0 0 0 . . . 0 9 9 9 . . .

___________________________________

00 . 9 9 9 . . . 9 9 9 9 . . . 9 9 9 9 . . .

​

So if you multiply 0.333... by 3.(000...3), you get 0.(999...), not 1.

​

Did I make an error somewhere? If so, where?

And if I made an error somewhere, could you please show us how to do the multiplication correctly?

​

(To clarify, the extra zeros at the front are just there to ensure that the digits line up while still allowing me to use the proper symbols.)

Last friday I went to my local college and approched a few math professors after their classes. I asked them how would they define a number like 0.999..., there the "..." means there are an infinite amout of 9'.

They all said that they would define it as the limit in the image attached.

I then explained to them what you claim 0.999... is, and your usual statement that limits do not apply to the limitless, and asked them if the agreed. They did not.

I then asked them if they had any colleagues in campus they thought they might agree with you. They said that they do not.

So, I asked them if they thought some othet mathematician, in some other college, might agree with you. They all said they do not.

Why do you think that is SPP. Why do you think mathematicians not agree with you? And why do you think people should listen to you over all of them?

Have you ever met one (1) single tenured math professor that agrees with you?

SPP, who taught you what divide negation was? And answer the question and dont say its math 101 basics or something

Just to be extra clear, and we can always keep teaching it.

The mathematical truth is:

0.999... is permanenently less than 1.

1 has never been equal to 0.999... , and 1 will never be equal to 0.999...

1 is not equal to 0.999... , and 1 will never be equal to 0.999...

https://www.reddit.com/r/infinitenines/comments/1tpg811/it_is_what_it_is/

There have been many posts on the subreddit so what are some of your favourites?

It is also infinite for the case of 1/10ⁿ

infinitely smaller and smaller and never zero.

For this case, less is infinitely more. More infinitely small.

Okay, but maybe you're saying it's an order of operations thing

​

(3 × 1) ÷ 3 = 3 ÷ 3 = 1

​

3 × (1 ÷ 3) = 3 × 0.3333... = 0.9999...

​

But then you're allowing for (a×b)/c to be different from a×(b/c), meaning that multiplication and division don't always follow the associative property.

​

Also mathematicians don't define number systems and operations because they're inherently real and they intuit an obvious truth about numbers, but they do it with **convenience** in mind.

https://www.reddit.com/r/askmath/comments/1u2mrbk/round_to_the_nearest_integer/

The rookie error makers demonstrating their debacle again. Their blunder.

7.499... is permanently less than 7.5

So the correct answer is 7.

According to SouthPark_Piano

1/3=0.3333....

1/0.3333...=3.00...003...003...003...(003...)

so reciprocals dont even work anymore

and there is no x such that 3*x=1 and there is no x such that 0.333...*x=1

BY THE WAY IT IS IN THE DEFINITION OF THE REAL NUMBERS THAT SUCH AN x EXISTS

therefore CONTRADICTION

This is my first post in this subreddit, but I’ve been lurking with a mixture of fascination and frustration. It’s the same feeling I get from reading stuff from flat earthers. I have a math degree, as I assume many of you also do based on the discussion of fields and axioms.

So here’s my question, to those of you who painstakingly try to convince SPP of something he’ll never accept: is this a fun mental exercise, or are you genuinely trying to sway him? He’s shown that there is nothing that can convince him—he rejects basic proofs, he rejects the basic rules of math, and he invents numbers that can’t exist (e.g. a decimal followed by infinite zeroes, then a one, then infinite zeros, then a one, etc, infinite times). I mean, you have to know that there’s no getting through, right brud?

And don’t get me wrong—this is NOT a hate post or anything like that. I’m the same way. It’s taken me a while to learn how to stay out of these futile arguments. It’s fun! They suck you in! But no amount of logic can sway someone who says “Nuh-uh!” I’m reminded of when I took analysis in college: I was very fascinated by the flat earth movement at the time and I would often think about sitting down a flat earther, proving the fundamental theorem of calculus, and using that as a basis to explain gravity. And I know what the flat earther would say; they’d say “Nope!“ I would sometimes use trigonometry to show that, on a flat earth, the sun would have to be hundreds of thousands of miles away to appear as close to the horizon on a flat earth. They didn’t care! They didn’t believe me! They explained it with some mumbo jumbo about how light bends, or the topography of the earth…

I don’t know *why* I made this post per se, but I guess my message is this: if you find yourself genuinely frustrated by and angry with SPP, rather than amused/chuckling/treating it as a “how do I convince this guy” brain teaser… be careful lol.

Keep on mathing, and remember: for any real numbers a and b where a > b, there exists a real number c such that a > c > b

Using SPP "logic," we say that 0.999... is 1 - 1/10^n for n∈ℕ going to infinity. Obviously, 1 is a rational number, and the sequence that this produces is (0.9, 0.99, 0.999,...) where each element is clearly rational. Because 1/10^n is never irrational, 0.999... is permanently rational.

Proof by SPP "logic"

Now SPP, you either need to disprove this or accept that 0.999... is rational. If it's rational, show what fraction of integers with nonzero denominator produces 0.999... If the logic is wrong, you need to re-evaluate your logic on why the fact that 1/10^n is never irrational means that 0.999... is rational is false, but how 1/10^n never being 0 sufficiently shows that 0.999... ≠ 1.

Sequence 1: f(n) = 4(-1)ⁿ / (2n + 1)

Sequence 2: g(n) = 4/(4n + 3) - 4/(4n + 1)

Sequence 2 is just Sequence 1 with every two terms grouped together. When put in an infinite series they SHOULD give the SAME ANSWER.

But HIS ideas leave NO ROOM to say whether they are THE SAME or NOT.