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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 ? | |||||||||||||||||||||||||||
Straggler Member (Idle past 95 days) Posts: 10333 From: London England Joined: |
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). It is the difference between an obtainable destination and that which can never exist or be obtained in reality. 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? Edited by Straggler, : No reason given.
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Son Goku Inactive Member |
PaulK writes:
This is a good point. Any changes you could make to the definitions used in mathematics to avoid 0.999... = 1, would also cause Calculus to stop working. More on the weird properties of real numbers in the next post....
In fact we needed this definition to deal with the sums of infinite sequences. And if we couldn't do that, integration wouldn't work (and we'd need to find a physical solution to Zeno's paradox, too !) So it is important to mathematics that 1 and 0.999... are the same number. If they were different we'd have real problems.
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Son Goku Inactive Member |
An interesting generalization of this is:
If any number with an infinite number of digits after the decimal point and has a repeating pattern in those digits, then that number has a finite number of digits in some base. From this you can prove that such numbers can be written as fractions. These are known as rational numbers. However pi = 3.1415....., cannot be written as a fraction and so has an infinite number of digits in any base. These are known as irrational numbers Finally and strangest of all, irrational numbers are more common than rational numbers. Edited by Son Goku, : Added repeating to first paragraph.
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bluescat48 Member (Idle past 4219 days) Posts: 2347 From: United States Joined: |
However pi = 3.1415....., cannot be written as a fraction and so has an infinite number of digits in any base. These are known as irrational numbers Finally and strangest of all, irrational numbers are more common than rational numbers. One more thing, there are 2 types of irrational numbers: Algebraic such as the square root of 2 which can be found by simple algebra or can be formed by a compass and straight edge. Trancendental numbers such as pi & e(base of the natural logarithms) which can't. As for more irrationals, this is logical since any rational number can be multiplied by pi or e or both, or by 1/pi, 1/e, pi x e, pi/e, e/pi, or 1/(pi x e), not to mention such things as pi**n, e**n or their reciprocals. Edited by bluescat48, : typooos There is no better love between 2 people than mutual respect for each other WT Young, 2002 Who gave anyone the authority to call me an authority on anything. WT Young, 1969 Since Evolution is only ~90% correct it should be thrown out and replaced by Creation which has even a lower % of correctness. W T Young, 2008
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Son Goku Inactive Member |
bluescat48 writes:
Yes and Transcendentals are more common than rationals and algebraic irrationals put together. Vastly more common. In fact almost all numbers are transcendental.
One more thing, there are 2 types of irrational numbers: Algebraic such as the square root of 2 which can be found by simple algebra or can be formed by a compass and straight edge. Trancendental numbers such as pi & e(base of the natural logarithms) which can't.
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RAZD Member (Idle past 1434 days) Posts: 20714 From: the other end of the sidewalk Joined: |
Hi Son Goku,
Yes, π is a fun number, no matter which base you use. Another one that shows up in a lot of natural systems is the golden ratio
_ Page not found | Geophysical Institute
quote: It is also the ratio of the "diagonal" of a pentagram to the side ... (now you can graphically draw a perfect pentagram without ruler or calculator). We have a member on this forum that uses it as his ID. Enjoy. we are limited in our ability to understand
by our ability to understand Rebel American Zen Deist ... to learn ... to think ... to live ... to laugh ... to share. • • • Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click) • • •
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MatterWave Member (Idle past 5059 days) Posts: 87 Joined: |
quote: So infinity and 1 are one and the same? Sounds exactly like quantum theory - the wavefunction of, say a human body, goes to infinity(overlapping other wavefunctions). The hard question is why do we always see 1 human instead of an infinite human? Do you have a personal philosophy on this? Edited by MatterWave, : No reason given.
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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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cavediver Member (Idle past 3672 days) Posts: 4129 From: UK Joined: |
Finally and strangest of all, irrational numbers are more common than rational numbers. More common... And in other news, Graham's Number is quite big
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cavediver Member (Idle past 3672 days) Posts: 4129 From: UK Joined: |
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 can't believe* it falls to me to raise (again - see my first post in this thread) that this identity is non-existent in finitism, and much of constructivism in general. All the mathematicians here are assuming that infinite decimals such as 0.9999~ actually exist. This is not a trivial point. *I hate constructivism, and wouldn't even mention it other than in derision - except that everyone seems to be assuming it doesn't exist, and it should be brought up for completeness. A very good friend of mine is a finitist, and it generally means we have very little to say to each other mathemtaically! His taste in music is also crap
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Dr Jack Member Posts: 3514 From: Immigrant in the land of Deutsch Joined: Member Rating: 8.3 |
Surely the difference between 0.999R and 1 is practically non-existant and philosophically massive? Nope, they're completely the same, philosophically and otherwise.
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). It is the difference between an obtainable destination and that which can never exist or be obtained in reality. Nope. There is no uncertainty, 0.9999~ is 1. In fact all decimal representations are infinite sequences, it's just some of them finish in an infinite number of 0s. This is not, as it may sound, a cute aphorism but actually fundamental to the construction of the real numbers. Real numbers are limits of inifnite sequences.
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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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Shield Member (Idle past 2891 days) Posts: 482 Joined: |
Thats a damn good guess seeing as there are hundreds of phenethylamines! You came close, it was 2c-E.
Lasts a couple of hours more than 2c-I and it is way more intense. But this is completely OT, and i dont think i have anything to add to the topic.
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cavediver Member (Idle past 3672 days) Posts: 4129 From: UK Joined: |
Nope, they're completely the same, philosophically and otherwise. I have to disagree here for the reasons I gave above.
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