[just4kickz]

Originally Posted by jaiman

2 or -2 jumps to mind.

isnt it assuming that its + or -? it really depends on the problem...but yeah that was what i was thinking...

[Hawkeye]

Originally Posted by just4kickz

but this is correct... and what is the square root of 4 then?

It could be either +2 or -2 so you cannot assume it is just 2, even though you do at a younger age in order to learn the concept.

[s1eepy]

Originally Posted by TurboFan

Not quite. First, you didn't use "x..." in the opening equation. Second, you've failed to tie your geometric series to the original question. I'd say you'll end up dividing by zero somewhere along the way.

But, thank you for an intelligent post! It's always nice to have a polite intellectual discussion.

More quite than not.

I was just using x… to represent 0.333…, 0.666…, or 0.999… in my example.
Secondly, I didn’t think there was need to explain how the series ties in, but that, and the ellipsis (…) denotes that the numbers I’m using have an infinitely recurring decimal, so there is no rounding error as thought by another poster, because there is no rounding. 1/3 = 0.333… is not an approximation, but exact. besides the fact that you can’t round a number with an infinitely recurring decimal, 0.333… is defined as the limit of the sequence (0.3, 0.33, 0.333, …)
Take that limit and you will get 1/3
Now use 0.999… and take the limit of that corresponding sequence and see what you come out with

[s1eepy]

Originally Posted by AndrewAZ

.99999 repeating moves closer and closer to 1 but never hits one it just gets closer and closer. Numbers are a concept by man mans concepts have flaws in them and this one is hard to grasp but if you keep adding .999999999 and keep adding 9's it will get closer and closer to 1 but will never = 1.

the problem with your assumption is that you are using the decimal to be a process of constantly adding more 9’s. By definition, decimal expressions and limits are not processes, but actual numbers, so there is no “adding 9’s”

[TurboFan]

Originally Posted by Kilockel

I say you start a new thread for it! I'll be sure to be there!

By the way... You're saying a sound wave, or something that has produced a sound wave, is not necessarily sound, or doesn't necessarily create sound?

I'm not under the impression that because we are unable to "feel" and interpret the waves, they cannot be classified as sound.

That being said... Nothing I don't personally agree with exists. Every concept I think of is inherently correct. "I haven't been wrong since 1961, when I thought I made a mistake."

Well, as I said earlier, what is sound? Everyone I know defines sound as something they hear. For you to hear, something must cause your ear drum to vibrate, which the nerves in your ear then carry to the brain where you interperate it as "sound". Usually sound waves cause the ear drum to vibrate, but vibrations can be carried through your body also causing your eardrum to vibrate.

[TurboFan]

Originally Posted by Hawkeye

You also learn that the square root of 4 is equal to 2. But that is not correct either.

well, it's half the answer.

[ages944]

As far as is necessary, sound is a bunch of pressure waves within a medium. If there was no medium, there would be no sound. Since there is, a sound is produced. Whether or not someone/something is there to perceive it is irrelevant.

[DesiGUY]

Originally Posted by Hawkeye

1 factorial is just equal to 1, not .9999

Again, this is about infinity which is not a solid concept to start with.

Tis not 1 factorrial...

1 != 0.999...
1 not equal to 0.999...

[GAM3OVR85]

1+1= 1 its easy

[GAM3OVR85]

hahaha.......jk!!

[TurboFan]

Originally Posted by ages944

As far as is necessary, sound is a bunch of pressure waves within a medium. If there was no medium, there would be no sound. Since there is, a sound is produced. Whether or not someone/something is there to perceive it is irrelevant.

so you are defining sound differently than I. I don't equate pressure waves to sound. Say those pressure waves were....oh, 10 Hz. Would they be sound?

[AndrewAZ]

Originally Posted by s1eepy

the problem with your assumption is that you are using the decimal to be a process of constantly adding more 9’s. By definition, decimal expressions and limits are not processes, but actual numbers, so there is no “adding 9’s”

Math has rules that govern it.. What the OP asked if .9999999999999 repeating to infinity was = to 1. And the answer is no it gets closer and closer to 1 but never reaches it such as an asymptote.

[jaiman]

a simple proof:
x = 0.9999...
10x = 9.9999...
10x - x = 9.9999.... - 0.9999....
9x = 9
x = 1

The assumption here being that there are infinitely many 9s after the decimal place.

[AndrewAZ]

Originally Posted by jaiman

a simple proof:
x = 0.9999...
10x = 9.9999...
10x - x = 9.9999.... - 0.9999....
9x = 9
x = 1

The assumption here being that there are infinitely many 9s after the decimal place.

Lets seee... 10x-x.... X=.9999 so 10(.9999)= 9.999 now 9.999 - x (x being defind as .9999) So 9.999-.9999= 8.999.

Your proof is simple but wrong, and tries to use rounding.

The reason we can not accurately calculate a circle is because of rules of multiplication and rational numbers, one can only estimate. Thus this is where the problem of .999=1 comes from is trying to multiple non irrational numbers.


Again .9999 is less than 1 so is .99999 and keep adding 9's as the OP suggest of an infinitely repeating decimal and it will always be less than 1.

[jaiman]

Originally Posted by AndrewAZ

Lets seee... 10x-x.... X=.9999 so 10(.9999)= 9.999 now 9.999 - x (x being defind as .9999) So 9.999-.9999= 8.999.

Your proof is simple but wrong, and tries to use rounding.

the dots after the 9 indicates that the sequence of 9s goes off infinitely. There is no rounding.

Here's a question for you what's infinity + 1 ? If you can't answer that then you won't understand this proof.

[Year's_End]

You guys are making this so much more complicated than it is. Just sayin.

[ages944]

Originally Posted by TurboFan

so you are defining sound differently than I. I don't equate pressure waves to sound. Say those pressure waves were....oh, 10 Hz. Would they be sound?

I'm simply removing perception as a prerequisite, and focusing only on the causal relationship between tree, air, and the resulting pressure waves. Whether or not we can perceive the waves, or were present to perceive them does not affect whether the pressure waves actually existed or not.
... Quantum Entanglement doesn't quite apply in this case.

Anyway, the tree falls, which in turn accelerates air molecules, which get manifested as pressure waves. If some of those waves are within a certain frequency range and happen across the eardrum of some schmo, then said schmo would register those pressure waves as a 'sound.' More interesting is that the elephant standing next to the schmo (hey, why not) would hear a much more complex sound, as that animal's acoustic range is wider (goes almost down to the 10Hz you mentioned). So, we'd have two quite different perceptions of the exact same phenomenon. I believe reality exists independently of our perceptions of it.

... there is no spoon

[TurboFan]

Originally Posted by ages944

I'm simply removing perception as a prerequisite, and focusing only on the causal relationship between tree, air, and the resulting pressure waves. Whether or not we can perceive the waves, or were present to perceive them does not affect whether the pressure waves actually existed or not.
... Quantum Entanglement doesn't quite apply in this case.

Anyway, the tree falls, which in turn accelerates air molecules, which get manifested as pressure waves. If some of those waves are within a certain frequency range and happen across the eardrum of some schmo, then said schmo would register those pressure waves as a 'sound.' More interesting is that the elephant standing next to the schmo (hey, why not) would hear a much more complex sound, as that animal's acoustic range is wider (goes almost down to the 10Hz you mentioned). So, we'd have two quite different perceptions of the exact same phenomenon. I believe reality exists independently of our perceptions of it.

... there is no spoon

A perfect support for my argument of "no". If no "schmo" is there, or an elephant for that matter, to convert the pressure waves to sound, then the tree did not make a sound.

Similarly, if the tree fell in a vacuum, would it make a sound, even if said schmo and elephant were standing there?


Quantum physics were only mentioned becuase I didn't want to get into the argument of "is the tree still there if you're not there to observe it".

[Kilockel]

Originally Posted by jaiman

the dots after the 9 indicates that the sequence of 9s goes off infinitely. There is no rounding.

Here's a question for you what's infinity + 1 ? If you can't answer that then you won't understand this proof.

Well, technically "infinity + 1 = infinity + 1", however this doesn't work in my opinion. You can't really add something to infinity, as there's no point, and no way to actual do it, or reason to. The answer will be the same.

Infinity + 1 = Infinity

You shouldn't be able to just say you're going to add one to infinity.

[Kilockel]

Originally Posted by AndrewAZ

Math has rules that govern it.. What the OP asked if .9999999999999 repeating to infinity was = to 1. And the answer is no it gets closer and closer to 1 but never reaches it such as an asymptote.

The difference of 1 and 0.999... is considered to be 0. Two numbers are considered identical if (and ONLY if) their difference is equal to 0.

[Kilockel]

Originally Posted by TurboFan

A perfect support for my argument of "no". If no "schmo" is there, or an elephant for that matter, to convert the pressure waves to sound, then the tree did not make a sound.

Similarly, if the tree fell in a vacuum, would it make a sound, even if said schmo and elephant were standing there?


Quantum physics were only mentioned becuase I didn't want to get into the argument of "is the tree still there if you're not there to observe it".

In your views, where sound is only considered sound if something or someone is there to interpret the waves, no, the tree does not make a sound.

In my views, where sound is considered sound if there are sound waves present (regardless of perception by anyone/anything), yes, the tree does make a sound.

It all lies in what you believe!

[jaiman]

Originally Posted by Kilockel

Well, technically "infinity + 1 = infinity + 1", however this doesn't work in my opinion. You can't really add something to infinity, as there's no point, and no way to actual do it, or reason to. The answer will be the same.

Infinity + 1 = Infinity

You shouldn't be able to just say you're going to add one to infinity.

exactly, just like infinity x 10 is still infinity, thus an infinite series of 9s after a decimal place, multiplied by 10 is still an infinite series of 9s after the decimal place.