does 1=0.999... ?

[Kilockel]

Originally Posted by Crimson92

this forum is odd at times

I'm going to have to agree!

[m0n0x!de]

Math sucks! But i still love it!:P

[TurboFan]

Originally Posted by Kilockel

Well, theorists probably isn't the right descriptor...

Everyone (I'm generalizing) knows:

1/3 = 0.333... (where "..." represents an infinitely repeating sequence)

That's simple enough, right? Lets multiply it by three!

3 x 0.333... = 0.999...

Well, that makes sense, doesn't it? So how about this?

3/3 = ?

You just did the math, didn't you? Three thirds is equal to 0.999...! How can that possibly be?

Basically it boils down to the concept of an infinite number, and the fact that two numbers are considered identical if (and ONLY if) their difference is equal to zero. Given any positive value, the difference between 1 and 0.999... is less than this value (this can be demonstrated using some complex maths that I'm not interested in posting). Thus the difference is 0 and the numbers are identical.

This is such a trivial anomaly that it's widely accepted that any mathematical procedure ending in 0.999... is considered to be 1. (This last bit is just my interpretation, and quite possibly over-simplified and incorrect. Take it with a grain of salt.)

My first quarter in engineering required us to take a class called "Numerical Analysis". All kinds of crap like this. I've worked hard to remove those memories, and you've just brought all of the flooding back. Thanks!

[Kilockel]

Originally Posted by TurboFan

My first quarter in engineering required us to take a class called "Numerical Analysis". All kinds of crap like this. I've worked hard to remove those memories, and you've just brought all of the flooding back. Thanks!

That's what I'm here for! If you have any other classes you've worked hard to forget, let me know and I'll try my best to bring you right back!!!

[TurboFan]

Sure,
EE743 - Dynamic analysis of electromotive motion device,
ME570 - Statistical methods and design of experiments
Phys512 - Electronics lab - actually a fun class, got to blow shit up
ME634 - Advanced control theory and mechatronics. Taught by the dude that designed the controls for Sputnik.
Psych 100, Soc101, Classics222 - damn I hated the gen-ed classes!


Shit, I just got a migrane. Time to go home.

[phantom330]

I have a better one.....


"if a tree falls in the forest and nobody is around to hear it, does it still make a sound?"


That one has been bothering me for years now. Any ideas?

[TurboFan]

Originally Posted by phantom330

I have a better one.....


"if a tree falls in the forest and nobody is around to hear it, does it still make a sound?"


That one has been bothering me for years now. Any ideas?

It depends on what you define as sound.

To me, it generates sound waves, that is indisputable without discussing Heisenberg's uncertainty principle and Einstein and othes theories regarding relativity.

However, SOUND is something we define as soundwaves being incident on our ear drum, and that vibration is translated by our brains. So no, it does not make a sound, but as defined by classical physics it does produce sound waves.

I've always enjoyed this debate, and I've heard some really interesting thoughts. I'm curious about yours.

[Hawkeye]

Originally Posted by Kilockel

Well, theorists probably isn't the right descriptor...

Everyone (I'm generalizing) knows:

1/3 = 0.333... (where "..." represents an infinitely repeating sequence)

That's simple enough, right? Lets multiply it by three!

3 x 0.333... = 0.999...

Well, that makes sense, doesn't it? So how about this?

3/3 = ?

You just did the math, didn't you? Three thirds is equal to 0.999...! How can that possibly be?

Basically it boils down to the concept of an infinite number, and the fact that two numbers are considered identical if (and ONLY if) their difference is equal to zero. Given any positive value, the difference between 1 and 0.999... is less than this value (this can be demonstrated using some complex maths that I'm not interested in posting). Thus the difference is 0 and the numbers are identical.

This is such a trivial anomaly that it's widely accepted that any mathematical procedure ending in 0.999... is considered to be 1. (This last bit is just my interpretation, and quite possibly over-simplified and incorrect. Take it with a grain of salt.)

Actually you are wrong. saying 1/3 = .3333... is the same thing as saying 1=.999999....

1/3 is actually equal to 0.333.........(1/3) If there is not an exact 1/3 at the end of the repetitive 3's it is not actually equal to 1/3.

This is a concept that does deal with infinity, and the basic conclusion is that 0.9999... = 1.

Thrying to prove a problem by using part of the problem itself is just stupid... and against basic matematic principals.

[Hawkeye]

Originally Posted by DesiGUY

Pure mathematically: 1 != 0.999...

Everywhere: 1 = 0.999... (if you wanted it to be)

1 factorial is just equal to 1, not .9999

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

[Kilockel]

Originally Posted by Hawkeye

Actually you are wrong. saying 1/3 = .3333... is the same thing as saying 1=.999999....

1/3 is actually equal to 0.333.........(1/3) If there is not an exact 1/3 at the end of the repetitive 3's it is not actually equal to 1/3.

This is a concept that does deal with infinity, and the basic conclusion is that 0.9999... = 1.

Thrying to prove a problem by using part of the problem itself is just stupid... and against basic matematic principals.

As was stated earlier, those were VERY basic examples. If you want to get into the gritty details and the interesting equations, that's fine. The result will be the same.

[Kilockel]

Originally Posted by TurboFan

It depends on what you define as sound.

To me, it generates sound waves, that is indisputable without discussing Heisenberg's uncertainty principle and Einstein and othes theories regarding relativity.

However, SOUND is something we define as soundwaves being incident on our ear drum, and that vibration is translated by our brains. So no, it does not make a sound, but as defined by classical physics it does produce sound waves.

I've always enjoyed this debate, and I've heard some really interesting thoughts. I'm curious about yours.

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."

[phantom330]

Originally Posted by TurboFan

It depends on what you define as sound.

To me, it generates sound waves, that is indisputable without discussing Heisenberg's uncertainty principle and Einstein and othes theories regarding relativity.

However, SOUND is something we define as soundwaves being incident on our ear drum, and that vibration is translated by our brains. So no, it does not make a sound, but as defined by classical physics it does produce sound waves.

I've always enjoyed this debate, and I've heard some really interesting thoughts. I'm curious about yours.

That explains it all. My guess was it still made a sound, because you have to imagine there are animals around to hear it. But I guess the next question is if the animals hear and process the sound like we do. It's all too much for me to think about, I'm gonna go back to simple mathmatics, or maybe I'll just forget about them both and move on with my life

[Year's_End]

1 = 1

end of story

[O-cha]

Take calculus man.

[Kilockel]

Originally Posted by Bimmer Loyalist

1 = 1

end of story

1 = 1 is a true statement.

Maybe the original question should have been formatted slightly differently.

Does 0.999... = 1?

[just4kickz]

lol... you learn this in middle school

[Hawkeye]

Originally Posted by just4kickz

lol... you learn this in middle school

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

[SoYank]

Originally Posted by Hawkeye

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

Now you tell me after I got all those damned monkeys.

Originally Posted by Hawkeye

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

I once dropped my sliderule and ever after, 2 times 2 was 3.99. I just called it 4.

[just4kickz]

Originally Posted by Hawkeye

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

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

[jaiman]

Originally Posted by just4kickz

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

2 or -2 jumps to mind.

[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.

[E(@M#]

the same concept as vertical asymptotes....take elementary math courses and you will learn the all about them.....this thread is teh stoooopid