0.99999~ = 1 ?

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.

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....

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 numbersFinally and strangest of all, irrational numbers are more common than rational numbers.Edited by Son Goku, : Added repeating to first paragraph.

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, 2002Who gave anyone the authority to call me an authority on anything. WT Young, 1969Since 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

Yes and Transcendentals are more common than rationals and algebraic irrationals put together. Vastly more common. In fact almost all numbers are transcendental.

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 Which is the ratio of a rectangle where you make a square from the short side and the remaining rectangle is the same proportion. The greeks used this as a foundation in their architecture for "ideal" shapes.Page not found | Geophysical Institute

quote:

---

Cross-section of nautilus shell showing the growth pattern of chambers governed by the golden ratio.

---

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.

---

quote:

---

Yes, you are correct. 0.9999..... = 1. Equals exactly.

---

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.

Actually, the difference in both cases would be completely non-existent. 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. 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. But 0.999~ IS 1.

---

I hunt for the truthI 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

No. 0.9999~ does not equal infinity. It equals one. Just as 1.999~ equals 2 and so on. I don't know enough about quantum mechanics to answer that question. Perhaps Son Goku or Cavediver can.

---

I hunt for the truthI 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

More common...And in other news, Graham's Number is quite big

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

Nope, they're completely the same, philosophically and otherwise. 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.

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 truthI 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

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.

I have to disagree here for the reasons I gave above.