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Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
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Author | Topic: 0.99999~ = 1 ? | |||||||||||||||||||||||||||||||||
Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
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 handMy 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
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Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
Briterican writes:
I guess you are then, because they are. 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. 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 handMy 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
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Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
Stragler writes:
Actually, the difference in both cases would be completely non-existent.
Surely the difference between 0.999R and 1 is practically non-existant and philosophically massive? 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 handMy 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
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Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
MatterWave writes:
No. 0.9999~ does not equal infinity. It equals one. Just as 1.999~ equals 2 and so on.
So infinity and 1 are one and the same? 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 handMy 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
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Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
cavediver writes:
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 ) And in other news, Graham's Number is quite big. I hunt for the truth I am the one Orgasmatron, the outstretched grasping handMy 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
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Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
Straggler writes:
Yes, since they are the same.
Can it be shown mathematically that 1 - 0.999R is equal to zero? 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 handMy 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
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Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
Straggler writes:
That they are equal? Look through this thread, I'd say. Fair enough. Is there somewhere I can see the mathematical proof of that? 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 handMy 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
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Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
A very nice video related to this subject.
Link here I hunt for the truth I am the one Orgasmatron, the outstretched grasping handMy 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
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Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
Rrhain writes:
What is it about math that makes people go mad, anyway? Or is it simply mad people that practice math? It took Russell and Whitehead years to develop the proof and Russell nearly went mad over it. I hunt for the truth I am the one Orgasmatron, the outstretched grasping handMy 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
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Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
Phat writes:
Zeno's paradox that's called.
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? Given:
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:
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. (superman's infinite coconuts) - (captain marvel's infinite coconuts) = 0 Sounds logical to me, though it's probably completely wrong.
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Huntard Member (Idle past 2324 days) Posts: 2870 From: Limburg, The Netherlands Joined: |
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!
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