Does 0.999...=1?

It depends on the situation, individual and context.

0.999 of an inch to a Computer lathe is exact, but it must have a decimal place limit.

0.999 of a mathematical computation is not 1.

<b><font color=blue>Change the</font color=blue><font color=red> sig of</font color=red><font color=green> the week!</font color=green> </b>

<b><i>YES!!!!</i></b>
0.9999999(to infinity) <i><b>IS</i></b> equal to 1!!!
Go do a little high school Calculus and you will see....

See a real naked pic of Britney Spears <A HREF="http://www.geocities.com/stick_e_mouse" target="_new">here</A>!!!

As x approaches 1...

Rob
Please visit <b><A HREF="http://www.ncix.com/canada/index.cfm?affiliateid=319048" target="_new">http://www.ncix.com/canada/index.cfm?affiliateid=319048</A></b>

Multiply 0.999 x 1000 and multply 1 x 1000 and you tell me thats equal, you must be a retailer... In conclusion the answer is one!

Oh Iam so confussed now.



Medication helps

Let me say this a third time, it's not 0.999 that I'm asking about. It's 0.9... with <b>the nines repeating FOREVER</b>.

I know the correct answer to this; I'm just curious as to how many others do.

Lyrics. Wasted time between solos.

There you go!

Rob
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Thank you!

Thats what what I was trying to say, only I couldn't be bothered typing up all the 9999999 crap. I should have bothered, cause he nailed me.

<b> <font color=blue>They changed the sig of the week!</font color=blue> </b>

Here is a simplified theorem from number theory:

If there exists no explicitly definable number C between A and B, then A = B.

My question is if A = 1 and B = 0.9r, what is C? O.999..9991?

Lyrics. Wasted time between solos.

Crap. Sorry. My bad. It was one of those days.

That should be: "0.9(n) will always be 0.0(n-1)1 away from 1.", not, "0.9(n)9 will always be 0.0(n-1)1 away from 1." Oops.

But n is defined as, "Where n is the number of repetitions of the previous digit.", and for added clarification, this is as a character array, not as a number.

So if n is 3, then you get: for the 0.9r side, n is 3 repitions of 9 = '999' to give you '0.9999', and for the 0.0r1 side, n-1 is two repitions of 0 = '00' to give you '0.0001'. And indeed, 0.9999 is 0.0001 away from 1.

So the ONLY time 0.9r could EVERY equal 1 is if your means of calculation involved limits. And, as we know, mathematical limits, by definition, are accepted innacuracies. So any means of calculating that 0.9r equals 1 is doing so using an innacuracy.

Calculators and computers, having limited memory and thus limited decimal places, are perfect examples of computing values using innacuracy.

<pre>(Change sig of week!)
<b><font color=orange>AROOOOOOOOOOOOOOOOOOOOOOO!</font color=orange></b></pre><p>

slvr_phoenix is right on this one. Just because some math teacher showed you something he thought was cool based on some theory etc, when you come down to actual numbers and decimals which although 1/3= .3333333... it's simply because the two values do not perfectly correspond. There is an error there as there is and error with thinking that in a world dealing with real numbers 1 could be .9... It just can't be

My Jesus is whiter than your Jesus.

yes .9 repeating equals 1 and there is a proof to prove that!

so for those of you who say no they are not equal then you are obviusly ignorant of math concepts. Such is the concept of the number one. 1 is an abstract thing it's not really there! so the abstract number of .9 repeating forever equals the abstract number 1.

i'll prove it to you right now.. if i can remember how the proof goes.. heh

ok now do we agree that if we did this ...

1+1+1 would = 3 .. right?

what about .5+.5+.5 = 1.5 ? do we agree to that?

ok now do we agree that 1/3 = .333 repeating forever?

now add .3333+ .3333 + .3333 = .999999 forever .. right? since we agreed (assuming u did) that .5+.5+.5 = 1.5 and etc ... it can kinda look like this

.33333... = 1/3
+ .33333... = + 1/3
+ .33333... = + 1/3
-------------------
.99999... = 1 ... because 1/3+1/3+1/3 = 1.

i just proved it to you rather you wanna believe a proof is up to you.. even though it's like saying the world is flat even though we have proof it's somewhat sphericle(sp?)(technicly not exactly but close).




<A HREF="http://www.anandtech.com/mysystemrig.html?id=9933" target="_new"> My Rig </A><P ID="edit"><FONT SIZE=-1><EM>Edited by xxsk8er101xx on 08/31/01 08:18 PM.</EM></FONT></P>

it's .9 repeating forever where 1/3 = .3 repeating forever.. and if you add .333 repeating + .333 repeating forever + .3333 repeating forever that equals .999 repeating forever... unless you don't know your math and think 4+4 = 44? .333+.333+.333 = .999 thus .333 repeating forever + . 333 repeating forever +.333 repeating forever ='s .9999 repeating forever... and where 1/3+1/3+1/3 ='s 1
so .99999 repeating forever (meaning infinite not finite (1 to 5 is finite forever is infinite) ='s 1 due to substitution and proof where 1/3 = .3333... forever as in it never stops.



<A HREF="http://www.anandtech.com/mysystemrig.html?id=9933" target="_new"> My Rig </A><P ID="edit"><FONT SIZE=-1><EM>Edited by xxsk8er101xx on 08/31/01 08:16 PM.</EM></FONT></P>

He won't make it in any finite amount of time, no. But if the frog could jump an infinite amount of times, he'd make it.

How about this:

If it's three feet from the lily pad to the bank, and the frog can jump one foot at a time, he is able to jump 33.3r% of the distance. Does he not make it to the bank in 3 jumps? And is this distance not 3 feet, or 100% of the total distance?

Lyrics. Wasted time between solos.

Now you're comparing apples and oranges. That is just not right. Everyone knows Mangoes are the best!


<font color=red><i>Tomorrow I will live, the fool does say
today itself's too late; the wise lived yesterday

you must be really bad at math! IT IS NOT .9! you obviously have no concept of infinity!

<A HREF="http://www.anandtech.com/mysystemrig.html?id=9933" target="_new"> My Rig </A>

lol if he doesn't get it after that i dunno i think he's just playing stupid lol ....

makes you kinda wonder though of .9r = 1 ... does this mean with our current understanding of math and science is flawed by .0r that is zero but there is that little bit that can never be calculated correctly? hmmm ... like if we took something and made it infinite can our current math understandings calculate it correctly? i'm just thinking... maybe math isn't so perfect with infinite objects. Of course that thinking will never be accepted ebcause we are all so comfy with the current math understandings. There might not be much use for infinite objects, such a thing can hardly be understood...

what if in order to bend space to travel much faster like worm wholes you needed to infinitly calculate the energy levels to bend space? Or to even rip a hole in space in order to travel much faster and then close it back up without causing a black hole? The amount of energy would be infinit? by being off that little bit could kill it maybe and cause problems???? what about black wholes? it is said to have infinite space? I think i forget...

just thinking is all.. no flaming because this is how new stuff are discovered by philosophicly thinking of these things and later down the road when technology is more advanced they try it out.



<A HREF="http://www.anandtech.com/mysystemrig.html?id=9933" target="_new"> My Rig </A><P ID="edit"><FONT SIZE=-1><EM>Edited by xxsk8er101xx on 09/03/01 10:31 PM.</EM></FONT></P>

Well, all anyone can really say about our current understanding of math and science is that what we have works well enough for what we need it to do. It is constantly being improved upon though.

Lyrics. Wasted time between solos.

Heh, just take a little more of that medication you're on; I'm sure it'll all become clear.

Lyrics. Wasted time between solos.

lol ... thats cos your calculator can't do infinity lol!

just take the concepts .. if you take 1/3 of the pie and ad another 1/3 and another 1/3 that is 1 right? lol.. dude this is tought in 2nd grade!

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I know what's on the other side. I'll sell you the info for $50 .

Lyrics. Wasted time between solos.

here is something to blow your mind!

Does time exist outside the universe? Could it be that the end of the universe is where time gets slower and it would take infinit amount of time to reach the edge of the universe? Which makes you think what black holes really are? because time slows down just like my educated guess about the edge of the universe, is it that the black hole is part of the edge of the universe? Why is it that black holes have infinte amount of space? could it be that space (universe) is like a thin sheet of paper. Nothing but void below and on top. void being where nothing exist - time light people things nothing... now since none of it exist could it be that as you get closer to the black hole time slows down and when you reach a point where time no longer exist you just stop? or do you keep goin through the void? but what makes it have infinit amount of space? And because time slows down as you enter a black hole and i suggested that as you reach the edge of the universe time slows down, are they the same? Now what about the difference in gravity? could it be like a piece of papaer you poke a hole in it and run a marble across it and it drops through the hole? SO! i'm not suggesting that gravity is in space i'm suggesting that the void pulls it in like a vaccum? unlike the edge where there is no hole only that it's the end so no where to fall? hmmm maybe at the edge of the universe you get pulled in to because the void is the same? Now what about time? if the edge gets slower is it that the center of the universes time is much faster then the edge? I'm suggesting a variable difference of how fast time is from the center to the edge? which would explain why we cannot calculate the age of the universe accuratly without conflicting the age of the suns? That would be funny if the universe is only 7 days old from the center for example? Now what is above the sheet of paper or space? the samething? hmmm ....

so variable time from one end to the other where the edge is much slower then the center. Space is like a flat sheet of paper (even though it is a 4D space: up, down, left, right, time, no sound i believe, ... but easier to comprehend in a 2d playing field) and a black hole is nothing more then a rip in space where everything falls into void. If that was the case you could easily bend space like paper fold it up like, rip a hole and travel through it and then cover it up otherwise you would create one huge problem heh! The amount of energy would be infinit because the energy would need to stay to keep it from ripping open again and the amount would be pretty high heh...

heh just thinking ...

<A HREF="http://www.anandtech.com/mysystemrig.html?id=9933" target="_new"> My Rig </A>

Actually, having infinity - 1, infinity + 1, or even infinity ^ 2 is pretty easy to do.

Infinity is an abstract number, not a constant. Working with it is just like working with imaginary numbers. If you can't work with infinity in such a manner, then you're just limiting yourself. I know I have no problems working with infinity - 1. It's simply 1 less than whatever infinity is.

The whole reason why the concept of

is flawed is because the number of repititions towards infinity <b>aren't</b> being counted in the calculations. If n = 0.9r (where r is an infinite repitition), then 10n = 9.9r-1 (where r-1 is one less than the infinite repitition). If you properly keep track of the number of repititions using infinity as an abstract number, you'll find that the above formula will actually serve quite well to prove that 0.9r <b>doesn't</b> equal infinity.

So for anyone who can work properly with infinity, my previous statement still holds quite true. And for those who can't, well, your loss.

<pre>(Change sig of week!)
<b><font color=orange>AROOOOOOOOOOOOOOOOOOOOOOO!</font color=orange></b></pre><p>

If you want to be technical about a realistic scenario where the frog jumps half the distance every time, he will in fact make it. It can even be calculated. There is a fundamental limit to how small a jump the frog can make. Once he has this far to go, the next jump will have to carry him all the way, as that will be the smallest distance physically possible.

As for the purely mathematical scenario, infinity is not just a really really big number, it means, well, infinity. The frog would make it, if he COULD jump an infinite amount of times, but because he can only ever jump a finite amount of times, it's safe to say he'd never make it.

Basically, you can say that the frog would never make it, because it would require that he make an infinite amount of jumps.

Lyrics. Wasted time between solos.

You don't get it. The number of repetitions in 0.9r isn't going towards infinity. The number IS infinite.

Lyrics. Wasted time between solos.

Tell those who cannot add nor subtract from infinity to read Douglas Adam's books. Puts the whole concept in laymens terms. I'm working on the infinite improbability machine right now, the odds of me every finnishing are infinity to one.

Back to you Tom...