r/infinitenines

Rookie errors going on everywhere.

https://www.reddit.com/r/piano/comments/1fcak86/intervals_from_a_span_of_notes_perspective/

 

1 - 1/10^n with n integer starting from n = 1, and then n pushed upward continually limitlessly, aka pushed to positive infinity.

That golden expression accurately conveys the infinite aka never ending summation, the endless trek, the never ending journey, going where no one has gone before.

The golden expression, conveying officially known fact:

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

This is the voyage of infinite nines.

A mission ... to explore ... etc.

The gap magnitude difference between 1 and 0.999...9 aka 0.999... is 0.000...1 , which is 1/10^n with n pushed to positive limitless.

1/10^n is never zero.

So while the magnitude difference is 0.000...1, 1 - 1/10^n is never 1, ie. permanently less than 1.

0.999... is permanently less than 1.

This means 1 is never 0.999... , and 1 is always relately infinitely far from 0.999... , which some may say, so infinitely close and yet so infinitely far. And what matters is ..... 1 has never been 0.999... , and 1 will never be 0.999...

 

And is the contract necessary to reach the conclusion that 0.999...<1?

9.(9) is simply 0.(9)*10 also as said by SPP. Thus, 9.(9)=0.(9)*9. Additionally, 9.(9)-0.(9)=10*0.(9)-0.(9)=9*0.(9) by distributive property. 9.(9)-0.(9) is also equal to 9+0.(9)-0.(9)which is equal to 9. So, 9=9*0.(9). By the fundamentals of algebra, 1=0.(9).

0.999... is equal to 0.9 + 0.09 + 0.009 + ...

That is official fact.

The value is 0.999...9 aka 0.999...

Because 0.999...9 never runs out of nines, and because the continually increasing limitless length aka infinite length of consecutive nines just never stops increasing, the situation is that 0.999... simply just never 'reaches' 1. Because the gap 0.000...1 simply never goes away, 0.999...9 aka 0.999... is simply always relatively infinitely far from 1.

It is just not a case of 0.999... 'not quite reaching 1'. It is a case of 0.999... just being permanently less than 1. Which is the same as 1 never being 0.999...

0.999... is the star here. 1 is supporting cast member.

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Hello SPP.

I'm going to use x=0.999... (infinite nines) for shorthand.

Think about 9.999...

That is 9+x.

What is 9.999... divided by 10? Is it x?

To clarify, an axiom is a foundational assumption that is built off of via logical deductions.

As an example, we can set the following axioms to be true:

Axiom 1: a>0

Axiom 2: b>0

From these axioms, we can use a series of logical deductions to conclude that a+b>0. Here's how:

Step 1: a>0 (by Axiom 1)

Step 2: a+b>b (adding b to both sides preserves the inequality)

Step 3: a+b>b>0 (by Axiom 2)

Step 3: a+b>0 (by the Transitive Property of Inequality)

This is how axioms work.

Now what axioms do you set to be true in your system, and what logical deductions are made to conclude that 0.999...<1?

It's okay if you don't have all of your axioms ready to go. All I'm asking for is axioms and logical deductions that are sufficient to prove that 0.999...<1 within your system. We can worry about additional axioms later.

Obviously, and officially, 0.999... is equal to 0.9 + 0.09 + 0.009 + ... , which means limitless never ending aka infinite sum. Just never stops, never ends, this summing.

0.999...9 is symbolism for that summation, which is aka 0.999...

From the 1 perspective, in order to get 0.999... aka 0.999...9, a subtraction operation ... ie. operation, is required. An operation on the 1.

No operation, no 0.999... aka 0.999...9

0.000...1 is the dynamically reducing amount to be surgically removed from 1 to get 0.999...9 aka 0.999...

The overall operation is described aka conveyed as:

>!1 - 0.000...1 = 0.999...9 aka 0.999...!<

1 cannot ever reach 0.999...

Well ... not without an operation (a limbosic one) anyway. In which case, if 1 is operated on with a surgical subtraction tool, as in something removed from 1, then obviously it would not be 1 anymore.

Although SPP has made countless attempts to save them, they always seem to be infinitely out of reach, trapped in the Metamathemagical realm.

I want to ask them: How can we save you? What will it take to convince you? Is there any hope?

https://www.reddit.com/r/AskElectronics/comments/1umvkd4/comment/ovfvxpc/

See. Real deal maths does apply to both practical and impractical situations.

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Let’s say I have a spaghetti noodle where both ends are in my hand. I apply a function that determines the length of the rest of the noodle which trails away from me such that the midpoint is at or close to its furthest distance away from me.

{me}>
{me}=>
{me}===>
{me}===========>

Question:
If the noodle is infinitely long…

{me}==================…

…does that mean I have two noodles, or do I still just have one? Is there even a difference?

From a recent post ...

https://www.reddit.com/r/infinitenines/comments/1ulj8jw/comment/ov6vu93/

Stuff that most of youS were taught at school but ignored, which led to your rookie errors.

Set reference ...

x = 0.999...9 = 0.999...

Now writing one factual equation using math basics.

1/0.999...9 = 1 + 0.000...1 / 0.999...9

1 = 0.999...9 + 0.000...1

aka 1 = 0.999... + 0.000...1

aka (1/0.999...) × 0.999... = 1 aka divide negation.

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Hello friends, I have a question regarding a certain paradox, and I was wondering if someone could help me solve it.

Achilles and a tortoise enter a race. Since Achilles is faster than the tortoise, the tortoise gets a headstart.

When the race begins, Achilles must first reach where the tortoise was previously. But by the time he gets there, the tortoise has moved forward. So Achilles must then reach the tortoise's second position, at which point the tortoise has moved even further forward.

Intuitively, you would think that Achilles will win the race since he is faster than the tortoise. However, the analysis seems to show that Achilles can never catch up to the tortoise, let alone beat him in the race.

Can anyone help me solve this? Who wins the race?

And thus There is NO 1, as there no terminating 1 after there is no terminating 9.

(0.999... * 10) - 0.999... =\= X.XXXXX... 1

1 the one supposedly comes about when the last 9 that doesn't exist is subtracted from a zero.

Ba Bow.

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

Meaning it has not stopped.

How many digits does it have right now?