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Author Topic:   0.99999~ = 1 ?
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 1 of 237 (543076)
01-15-2010 8:19 AM


I've seen this thing come along a couple of times on the internet, and was curious what our local math guys think about this.
It is my understanding that 0.9999~ does indeed equal 1.
I could be wrong though.
So, any thoughts on this?

I hunt for the truth
I am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

Replies to this message:
 Message 2 by cavediver, posted 01-15-2010 8:42 AM Huntard has not replied
 Message 4 by Son Goku, posted 01-15-2010 9:00 AM Huntard has not replied
 Message 6 by LucyTheApe, posted 01-15-2010 9:15 AM Huntard has not replied
 Message 16 by Straggler, posted 01-15-2010 7:26 PM Huntard has replied
 Message 80 by Rrhain, posted 01-23-2010 4:45 AM Huntard has not replied
 Message 81 by Iblis, posted 01-23-2010 5:12 AM Huntard has not replied

  
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 5 of 237 (543083)
01-15-2010 9:04 AM
Reply to: Message 3 by Briterican
01-15-2010 8:49 AM


Re: Hmm, equal?
Briterican writes:
Shouldn't there be some sort of conditional involved or something? I don't see how it could be considered accurate to say that 0.99999~ is precisely equivalent to 1.
I appreciate that, for all intents and purposes, they are equivalent. But mathematically they simply are not, right?
Maybe I'm missing something.
I guess you are then, because they are.
If you don't think they are equal, try answering this question: "What is the difference between 1 and 0.9999~." If they are not equal, there should be a difference, no?
Also try this explanation
X = 0.9999~
10X = 9.9999~
10X - X = 9
9X = 9
X = 1

I hunt for the truth
I am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

This message is a reply to:
 Message 3 by Briterican, posted 01-15-2010 8:49 AM Briterican has seen this message but not replied

  
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 23 of 237 (543200)
01-16-2010 4:08 AM
Reply to: Message 16 by Straggler
01-15-2010 7:26 PM


Re: 1 and NOT 1
Stragler writes:
Surely the difference between 0.999R and 1 is practically non-existant and philosophically massive?
Actually, the difference in both cases would be completely non-existent.
It is the difference between claiming complete certainty (for example) and always allowing for the possibility of that which is unexpected (no matter how likely or unlikely).
No, for when you elave o pissibility open, there should be an end to you "string of nines" no matter how long it gets. Wit 99.9999~% however, that's not the case. Answer the question I asked Briterican if you think they are not the same number: "What 's the difference between 0.9999~ and 1". There should be a difference if they are not equal.
It is the difference between an obtainable destination and that which can never exist or be obtained in reality.
No, it's like saying: "I went to Constantinople" and "I went to Istanbul". They're both the same place, just different ways of writing them.
I am no mathematician. But surely the difference between 1 and NOT 1 is as significant as ever. No matter what the NOT 1 may be?
But 0.999~ IS 1.

I hunt for the truth
I am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

This message is a reply to:
 Message 16 by Straggler, posted 01-15-2010 7:26 PM Straggler has replied

Replies to this message:
 Message 26 by cavediver, posted 01-16-2010 5:28 AM Huntard has not replied
 Message 39 by Straggler, posted 01-17-2010 3:22 PM Huntard has not replied

  
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 24 of 237 (543201)
01-16-2010 4:13 AM
Reply to: Message 22 by MatterWave
01-16-2010 3:28 AM


Re: Totally right!
MatterWave writes:
So infinity and 1 are one and the same?
No. 0.9999~ does not equal infinity. It equals one. Just as 1.999~ equals 2 and so on.
The hard question is why do we always see 1 human instead of an infinite human? Do you have a personal philosophy on this?
I don't know enough about quantum mechanics to answer that question. Perhaps Son Goku or Cavediver can.

I hunt for the truth
I am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

This message is a reply to:
 Message 22 by MatterWave, posted 01-16-2010 3:28 AM MatterWave has not replied

  
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 28 of 237 (543214)
01-16-2010 8:17 AM
Reply to: Message 25 by cavediver
01-16-2010 5:20 AM


Re: Funny Properties
cavediver writes:
And in other news, Graham's Number is quite big.
Ah yes. Even if every digit were the size of only 1 planck volume, the observable universe would still not be big enough to contain a digital representation of it (or so wiki says )

I hunt for the truth
I am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

This message is a reply to:
 Message 25 by cavediver, posted 01-16-2010 5:20 AM cavediver has replied

Replies to this message:
 Message 33 by cavediver, posted 01-16-2010 10:22 AM Huntard has not replied

  
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 44 of 237 (543369)
01-17-2010 3:56 PM
Reply to: Message 43 by Straggler
01-17-2010 3:51 PM


Re: 1 and NOT 1
Straggler writes:
Can it be shown mathematically that 1 - 0.999R is equal to zero?
Yes, since they are the same.
One step further down the infinite chain than you need to go to make 0.999R the same as 1?
How many steps does an infinte chain contain then? And what is infinity + 1?

I hunt for the truth
I am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

This message is a reply to:
 Message 43 by Straggler, posted 01-17-2010 3:51 PM Straggler has replied

Replies to this message:
 Message 46 by Straggler, posted 01-17-2010 4:04 PM Huntard has replied

  
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 48 of 237 (543378)
01-17-2010 4:21 PM
Reply to: Message 46 by Straggler
01-17-2010 4:04 PM


Re: 1 and NOT 1
Straggler writes:
Fair enough. Is there somewhere I can see the mathematical proof of that?
That they are equal? Look through this thread, I'd say.
Otherwise, look it up on wiki, there are some nice proofs there as well.
Well is infinity + 1 > infinity.
More than infinity? How's that even possible?
I guess not.
Indeed. Infinity + 1 = infinity.
Have you heard of the Hotel with infinite rooms analogy? It goes something like this:
There is a Hotel that has an infinte number of rooms and an infinite number of guests. Now, one more guests checks into the hotel. How do they fit that guest into the hotel? Simple, they move all the guests one room, and the free room can now be occupied by the new guest.
Now, how many rooms does the hotel have? Still an infinite amount.
But even in my fairly limited context of undergraduate level physics (as opposed to pure or higher level maths) the concept of more rapidly approaching infinity and thus "degrees of infinity" has arisen. At least in some sort of conceptual principle.
Ah yes, there are more then one infinity.
Try this for a fun experiment. Take a circle, now, draw lines of infinitely small width from its center to its edge. How many lines are tehre? An infinite amount. Now, draw a bigger circle around it, and extend your lines outward to that circles edge. Suddenly there are spaces between the lines! But how can this be, if the lines are infinite?
So even if I am taking the role of the idiotic punchbag for the more mathematically literate here I do so on the basis of asking whether things are as obvious as you seem to be claiming?
Apparently, to math guys, they are.

I hunt for the truth
I am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

This message is a reply to:
 Message 46 by Straggler, posted 01-17-2010 4:04 PM Straggler has replied

Replies to this message:
 Message 50 by Straggler, posted 01-17-2010 4:31 PM Huntard has not replied

  
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 49 of 237 (543379)
01-17-2010 4:24 PM


On infinities
A very nice video related to this subject.
Link here

I hunt for the truth
I am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

Replies to this message:
 Message 51 by Briterican, posted 01-17-2010 5:00 PM Huntard has not replied

  
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 162 of 237 (544410)
01-26-2010 4:01 AM
Reply to: Message 161 by Rrhain
01-26-2010 2:13 AM


Rrhain writes:
It took Russell and Whitehead years to develop the proof and Russell nearly went mad over it.
What is it about math that makes people go mad, anyway? Or is it simply mad people that practice math?

I hunt for the truth
I am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

This message is a reply to:
 Message 161 by Rrhain, posted 01-26-2010 2:13 AM Rrhain has replied

Replies to this message:
 Message 164 by Dr Adequate, posted 01-26-2010 6:24 AM Huntard has not replied
 Message 182 by Rrhain, posted 01-27-2010 2:36 AM Huntard has not replied

  
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 187 of 237 (544562)
01-27-2010 5:09 AM
Reply to: Message 186 by Phat
01-27-2010 4:20 AM


Re: Im puzzling myself
Phat writes:
This reminds me of the problem, (I forget the exact name) where the tortoise runs half as far as the hare....does anyone remember it?
Zeno's paradox that's called.
Given:
1) Captain Marvel and Superman operate at the exact same speed.
2) Superman always deposits 2X as many coconuts in the pit as does Marvel take out.
3) Time can be divided into infinitely small units of measure, and Superman and Marvel both can keep up the pace.
Does it not then follow that for any given unit of time (T) there will always be 2 coconuts in and one coconut out? Thus, even if every single coconut can be accounted for by a number, there is always at that same moment a number twice as great going into the pit...thus at any given moment of time, X+X (or X+Y?) Coconuts are going into the pit, while either X or Y are coming out of the pit...leaving the contents of the pit always at some variable of X (or Y) be it 1X, 2X, google-X, or Infinity X.
The way I see it the problem is with the fact that there will be an infinite number of actions from both captain marvel and superman. given that there are an infinite number of times captain marvel will throw out a coconut, there will be no coconuts in the pit. the fact that superman throws in an infinite amount doesn't matter. In fact, maybe this helps:
(superman's infinite coconuts) - (captain marvel's infinite coconuts) = 0
Sounds logical to me, though it's probably completely wrong.

This message is a reply to:
 Message 186 by Phat, posted 01-27-2010 4:20 AM Phat has not replied

Replies to this message:
 Message 190 by Rrhain, posted 01-27-2010 6:44 AM Huntard has replied

  
Huntard
Member (Idle past 2324 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 191 of 237 (544567)
01-27-2010 7:04 AM
Reply to: Message 190 by Rrhain
01-27-2010 6:44 AM


What's also interesting is that in both cases, an infinite amount of coconuts have left the pit. Even when, in the second example, there is also an infinite amount left in the pit.
Oh infinities, what fun they are to boggle the mind!

This message is a reply to:
 Message 190 by Rrhain, posted 01-27-2010 6:44 AM Rrhain has not replied

  
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