u/trshxd

By your definition, .999... is a limitlessly growing process.

Meaning it has not stopped.

How many digits does it have right now?

Hi,

u/SouthPark_Piano I took a deep breath and recollected myself after making so many of those typical rookie errors we all make (except you, of course).

I believe I might be a step closer to understanding methematics.

But I can't grasp the idea of infinity quite right yet.

What is infinity? Does it have a value? Is it somehow bound to the time itself? Does it change? Does it have a start and no end, or does it not have a start nor an end?

You answering my question(s) would be much appreciated, I'm starting to believe it all makes sense.

Thank you and have a nice day

u/SouthPark_Piano in this comment you state that there is a wrong way and a right way of using limits.

Please, explain the difference between those ways and give an example. When would you use a limit the right way?

And just to tease your brain a little:

You can't take a limit of a number itself. You can't take a limit of the number 0.999..., but you "the hell" can take a limit as n→∞ of the infinite sum (since it's an expression with a variable):

\sum_{n=1}^{∞}\frac{9}{10^{n}}

Or even of:

\sum_{n=1}^{∞}1-\frac{1}{10^{n}}

Which is, as you've previously said, the way you construct 0.999.... Now go and try to solve these limits on a calculator, and share the result with us, I'd like to see if your calculator has learned anything from you.

Note: put the text strings "\sum..." into a latex compiler to see the expression clearly.

Posting like this because SPP - again, cowardly - locked the comment.

SPP, now you listen, I'm gonna dumb it down for you, so you can actually try to have a counterpoint to anything in this post.

Your errors all come from misunderstanding what a number is.

A number is a representation of a value, a value that does not change. It's something one moment, and it's exactly the same something after one minute, after one hour, and after the universe's death.

Example 1:

3 - Three

The number 3 represents a certain value. The number 3 represents a single value in the real numbers (look it up on google if you don't know what that is).

The number 3 is not, in any way, dependent on time or any other physical quantity.

Example 2:

0.5 - Zero point five / point five / one half / nought point five

The number 0.5 also represents a single value in the real numbers.

The number 0.5 does not, in any way, depend on time or any other physical quantity.

Example 3:

0.999... - zero point nine repeating / point nine repeating, ...

The number 0.999... also represents a single value in the real numbers.

The number 0.999... does not, in any way, depend on time or any other physical quantity.

0.9999, 0.9, zero point million millions of nines are different numbers.

Why?

Because they are finite, they are terminating. The true 0.999... is not finite nor terminating. It has an infinite amount of nines after the decimal point.

And yet, it represents a single value. It's not a process that takes time to complete, nor is it a value that changes in any way, shape or form. It represents a single value, just like the numbers 3 and 5.

_____

You are right saying 1/10^n and 1/x are never zero. That's because those n or x are numbers (and integers - we'll get to that). They represent a single, finite value. Doesn't matter how big of a number the x in 1/10^x is, the expression will never be zero, because x will always be a finite number (an integer).

Let's get to the point.

0.999... can be represented as:

0.9 + 0.09 + 0.009 + 0.0009 + ...

Which (by your own words!) is an infinite sum. It could be written as:

\sum_{n=1}^{\infty} \frac{9}{10^n}

Note: put this string in any latex compiler to see the math notation.

Now - you like to describe it as:

"1 - 1/10^n with integer n starting at 1, then n upped continuously limitlessly aka infinitely"

Which is fine. Now look - can you show me an integer n that would make the expression equal to 0.999...? Note that it has to be an integer, since you describe it as such.

Let me guess - you can't show me such an integer, because it does not exist. Whichever integer (and there's plenty to choose from!) you put in as n, the result will always be finite and terminating. Doesn't that sound familiar? It does! That's the number 0.9999, or 0.999999999999999999, or zero point nine repeated million millions times!

And look, it terminates! It does not go on forever! But that is not what the true 0.999... is!

Hmm, you know what could be useful? We would like to somehow put ∞ (infinity) as n. But we can't do that, because ∞ is not an integer nor a number!! If we want to plug in the infinity so our expression can become the true non-terminating never-ending zero point nine repeating, we have to use something that's called a limit.

Let me show you a quick example:

lim x -> +∞ (x+x)

You know what this limit equals to? It is equal to infinity and I hope you can see why. If that's not clear to you, you can ask directly in the comments or you can try searching it online. Let's get back to our 0.999....

0.999... is an infinite sum. What is an infinite sum equal to? It's equal to the limit of it's partial sums. Partial sums are the little steps you make when doing an infinite sum - 0.9, 0.99, 0.999, ... are partial sums. There is an infinite amount of them. As we've made clear before, we can't put ∞ as n in our expression, because ∞ is not a number. We have to use limits to "put ∞ as our n".

That is the way we construct the true 0.999....

I know you're so eager to say "limits don't apply to the limitless". But -

Limits do apply to the limitless, because limits are what we use to define what happens at the infinite aka limitless scale.

Without them, we could not work with infinity, thus the 0.999... would be impossible to construct. If you talk about 0.999... and reject limits at the same time, you are not talking about the non-terminating never-ending 0.999... the rest of this sub talks about.

If you reject limits, your 0.999... terminates, which means it does not have an infinite amount of nines after the decimal point.

I'm open to discussion. Note that a discussion is a discussion only if all the sides participating have an opportunity to share their thoughts and reply to others. So, I ask you to not lock any comments under this post, especially not yours.

Don't show everyone in this sub that you don't understand basic math or what a discussion is. If you lock comments or reply with the same slop you always do (your description of 0.999... repeated a thousand times - you can't make it be true by repeating it), you are in no place to claim you "teach" us.

Have a nice day.

Hi. I'm still fairly a noob in minesweeper, although I can complete the expert board (Minesweeper - the clean one, so no guessing) in under 3 and a half minutes, most of the times.

I'm quite familiar with patterns, yet I still can't wrap my head around reduction.

Let's say i have a [2] touching at least 4 other tiles. I know that in 2 of them (let's assume they are right next to each other), there certainly is a mine, but I don't know in which tile from these two it is. Can the [2] be reduced into [1] and become a part of a pattern - e.g. a 1-2 pattern, so 2-2 becomes 1-2, even if I don't flag the mine in one of those tiles where the mine certainly is?

I'm sorry that I'm not showing a drawn example, which my clumsy writing makes much more inconvenient.

Thanks in advance, have a nice day.

Hi. I recently watched a YT short from mathandcobb (I was bored) which shows how a graph of a continuous function can have infinite length on a finite interval.

Does a function like f(x) = [1/(x - 1)^2] fit that criteria?

Since it's undefined at x = 1 and it's limit there is infinity, could it be argued that the graph of that function has infinite length on the interval (0, 2)?

I've never seen him ask a question to learn something. I don't mean those

Have you signed the contract?

Do you use your brain?

mock questions (even though I can't remember the last time SPP has asked any question, including these "insults").

He thinks that he knows it all yet we never see him trying to acquire new knowledge, or even asking in order to better understand what the person being asked means by their statements.

It's a pretty clear sign of his intellectual arrogance, narcissism and the Dunning Kruger Effect.

The 0.999... you talk about is not the actual 0.999... we talk about. Your 0.999... terminates, as implied by your statement from a recent post:

>where the pre-requisite number of nines that begins to qualify 0.999...9 is the largest number you can or cannot generate with your brain

The actual 0.999... is non-terminating - that means it has infinite amount of nines after the decimal point, not just "the largest number you can think of".

It never, at any point in time, has a finite number of nines. Example:

Let's say someone's brain can only generate a number that's no more than 10^1000. Does that start to qualify as 0.999...? No, it does not, because the number 10^1000 is finite.

Let's say someone's brain can only generate a number that's no more than 10^(10^1000). Does that start to qualify as 0.999...? No, it does not, because the number 10^(10^1000) is finite.

I hope you see the pattern.

Doesn't matter which integer you plug in as n , since an integer that would give you the actual 0.999... doesn't exist.

Note that it is very important to understand that infinity is not an integer. Remeber that bud.

Also, you correctly say that 0.999... = 0.9 + 0.09 + 0.009 ..., yet you incorrectly conclude that it does not equal to 1.

As you don't seem to know, an infinite summation is equal to the limit of the sequence of it's partial sums, but there is no point in teaching you this because you don't even understand limits.

-----

I'm curious about y'all's opinions on this - is the 0.999... SPP (and maybe some others) talks about the same as the 0.999... we talk about?

Edit: Sorry for the broken formatting.

I'm not from Australia or America, so I don't know how calculus 1 is called in other countries, but it's the subject where you learn about sequences, functions, derivations, integrals, a little bit of set theory, ... and most importantly, limits .

SPP has obviously been sleeping throughout all his lectures of calc 1. It makes him the last person that should teach anyone anything about the real numbers (which is the set of numbers we use when we talk about 0.999... ), yet alone infinitesimals.

SPP is a delusional liar that does not understand the subject he talks about, which makes him inadequate to be a person to listen to. He makes rookie errors aka dumb mistakes that even a first year uni student would point out and would teach SPP a lesson.

SPP, bud, go back and learn at the bunny slopes before you spit out nonsense, you'd do all of us a favour.

Sorry for the rant y'all, as I've said in my last post, SPP's arrogance and limited mind makes my blood boil.

Have a nice day.

Posting like this because SPP - again, cowardly - locked the comment.

SPP, is there anyone in this sub that genuinely thinks you are right with any of your "proof"?

Is there anyone you know of who's seen your statements and went "Oh, this guy is right!" ?

If so, can you name them?

 

>I don't need to 'come up with' anything new

You should, all of you statements have been proved wrong like million times. At this point it's just your limited mind that's holding you back from getting unstuck from your naive idea of you "teaching" us.

 

>when I have nailed your 'issue'

Oh bud, I'm not the one with 'issues'. You seem to be wildly obsessed with spitting out some made up nonsense left to right just to flatly refuse to have a fair discussion when someone points out your mistakes aka rookie errors aka blunders.

Do you genuinely not see the problem with your way of interacting with this community?

Sorry to y'all for the rant, sometimes SPP really makes my blood boil. Have a nice day.