Is 0.999999.... (infinite) equal to 1?

[frodo.rok]

About the topic I am in complete agreement with Vissin.

About infinity:
Mathematicaly, Lim (1/X) =infinity
X-->0

Physicaly, radius of the universe= infinity.

[suyash]

yes, according to abstract mathematical laws, it can be proved that 0.9999 (with infinite such 9's) will definitely be equal to 1 (as proved by raj87verma88)...

However, since the value of infinity can't be realized in real life, such an application is not possible for generating solutions to mathematical problems dealing with practical physics and other sciences

I might sound confusing, but then "God doesn't exactly play dice" , and there just might be some really great reason why we can't prove that 0.99999999 (till infinity) is not equal to 1 ...

[xheavenlyx]

I just could not hold myself here. Wow, amazing thread! And a long reply, so read it, if interested

I agree with Vissin 100.1111...%. Absolutely right. One of the best explainations!!!!

VISSIN:
0.999... = 3 * 0.333... = 3 * 1/3 = 1
ie. 0.999... = 1

What we prove is only to our abilities in science, we prove what we can perceive and measure. 1000 years ago we thought earth was flat till science proved otherwise. Anyway...

0.9999...inf. will equal to one depending on the perception of "0.99999...inf".

EXAMPLE: Radius of earth is 6,378.1 km or 6378.1 * 1000 * 100 * 10 mm= 6,378,100,000 mm so 6,378,100,000.99999... will also be 6378.1 km meaning we can accept it is equal to one when we are measuring a planet.

For some calculations we might need more accuracy and there we do not round it off till some numbers.

Depending on our use we can say 0.999999...inf is 1.

And biggie:

In my opinion, the moment you put an end to the series 0.999999......9... , it ceases to be equal to one.

I am hoping you dont mean this practically (theoretically maybe) because our cities and life is BUILT on these "inaccuracies" or approximations.

We dont say the car traveled 999.999998 meters but 1 km. We CAN say the ant traveled 999.999 meters OR 99999.90 cm because we MIGHT need more accuracy there.

I think Heisenberg's uncertainty principle explains it a bit too. May get confusing but keep reading it to understand.

...locating a particle (very accurately) (0.9999999...inf) in a small region of space makes the momentum of the particle uncertain; and conversely, measuring the momentum of a particle precisely makes the position uncertain (1 maybe? *smiles*).

On a side note I think we confuse INFINITE with "never ending, forever", which does not exist except the universe. INFINITE in science/math (I think) is used to say that in a particular case the value may be too much for consideration. For example Canada is "infinitely big" for a snail, because it will never traverse through east to west in its lifetime. Same way "Limits" in mathematics is for calculations where "approaching 0" means we are happy with it even if it is not, does not make a difference. If we need a zero then we recalculate.

[MaRo]

I have a deep feeling telling me that there's no infinity, it's just a concept but there a finite number.

DON'T CONSIDER, just a feeling

[The_Big_K]

This is getting even more interesting now

xHx, I'm talking about theory. I myself want to understand the concept ('concept') of Infinity in depth.

We dont say the car traveled 999.999998 meters but 1 km. We CAN say the ant traveled 999.999 meters OR 99999.90 cm because we MIGHT need more accuracy there.

That's right and explains my point.

For example Canada is "infinitely big" for a snail, because it will never traverse through east to west in its lifetime.

Good point. Extending on this logic, probably Universe is finite (okay, don't jump on me!) because its way too big for us to see what's at the end. I wonder if it has been mathematically proven that the Universe is infinite or its still a concept?

...and if universe is infinite, why do people say that its expanding? [Out of context; sorry for that!]

[vissin]

Originally Posted by frodo.rok

Physicaly, radius of the universe= infinity.

This and quite a few other posts here is speaking of the universe being finite or infinite. Here, I believe that we need to first understand what universe is. Another thread Big? I'll just give a few food for thought here as I don't want this post to be too long (and boring consequently)

While teaching lord Rama Ved Vashishtha spoke of many universes. Even today we speak of the many universes theory or the parallel universes. So in implication the whole expanse of the universe that we see as the universe is not all that's there.

If you believe in the big bang theory that inadvertently puts a limit to the size of the universe. Considering that the universe started expanding from one point and with the assertion that maximum speed attainable is that of light, if we know when the big bang occurred we can put an upper limit to the radius of the universe (d = s*t). We can find out when the big bang happened by studying the relative motion of galaxies and extrapolating it backwards to the center of the universe. I've heard of such figures as Universe being around 14 billion years old and the diameter of it being around 150 billion light years.

There is also a hypothesis that states that near big bang the matter coming out of the explosion probably traveled even faster than light.

[frodo.rok]

But is it feasible to take light speed constant at the time os Big Bang??
At Singularity(state of space time at the time of Big Bang where everything is concentrated in one point making space time INFINITELY curved) no physical law known to us holds.
So all this calculations are not trustworthy.
Isn't it??

[xheavenlyx]

Extending on this logic, probably Universe is finite (okay, don't jump on me!) because its way too big for us to see what's at the end. I wonder if it has been mathematically proven that the Universe is infinite or its still a concept?

...and if universe is infinite, why do people say that its expanding? [Out of context; sorry for that!]

Excellent point! basically we do not know for sure. depends on how far we can see in space and practical calculations on how galaxies are moving away from each other. Vissin also explains it well.

As for infinity, it should exist theoretically and it does not practically. I understand now what you were saying.

and frodo ur confusing urself and us, . The breakdown of physis laws at singularity is just a theory. and moreover that point in time was only once, so we cannot base much logic for current argument.

[frodo.rok]

If you believe in the big bang theory that inadvertently puts a limit to the size of the universe. Considering that the universe started expanding from one point and with the assertion that maximum speed attainable is that of light, if we know when the big bang occurred we can put an upper limit to the radius of the universe (d = s*t). We can find out when the big bang happened by studying the relative motion of galaxies and extrapolating it backwards to the center of the universe. I've heard of such figures as Universe being around 14 billion years old and the diameter of it being around 150 billion light years.--Vissin

extrapolating it backwards to the center of the universe--Vissin


Xeahavlynx I am sorry if I have made you confuse but as per as my knowledge Big Bang is a theory yet to be proved.So I can help it if THERE LIES CONFUSSIONS.
Now on extrapolating backward You will not find the same laws working if you have any faith on GENERAL THEORY OF RELATIVITY.
Suppose the universe is now at a state where it has a radius of say 5 km and it is expanding.
Just imagine everything lies in that sphere with radius of 5 km.
What will happen at this moment??
General theory of relativity tells us due to almost infinitely high gravitational force space and time will be so curved that every laws of physics get broken down.
d = s*t....This simple formula will not work at that moment.
Also if you say singularity is a hypothesis then i am afraid theory of Big Bang is no exception.
THE EXPANSSION OF UNIVERSE IS JUST LIKE A BALLON WITH DOTS IN IT.
When you start blowing it the the distance between the dots increases.
Just in case of our universe distance between Galaxis is increasing.
But in comparission to the Gallactic distance the radius of Universe will always appear to be INFINITE.

[vissin]

The discovery of the Cosmic Microwave Background (CMB) in the late 1960s gave tremendous boost to the Big bang theory and today it is the most widely accepted model of the Universe. Also General Theory of Relativity has only supported the Big Bang theory much to the discomfort of Einstein who believed in a static Universe.

The equation d = s*t has been proposed just to aid understanding and it's over simplification of the actual calculation. The Big bang has been divided into many stages called Epochs. The age and expanse of Universe has been calculated based on both Hubble expansion and CMB and has been found to be in agreement.

PS: The shape of the Universe is not very likely to be spherical. It might just be a lot flatter.