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I can't = impossible.Fluffy said:What do you mean by "not possible"? It is not possible for me to split this coke can into 83 equal parts but that does not mean it is impossible. Just because I lack the ability to split something an infinite amount of times does not make it impossible.
If 0.9^ did not equal 1, then there would be a number in between 0.9^ and 1, which there isn't.
The dictionary.Fluffy said:Do you have a reference for that definition?
No, I have produced three pieces of cake. Three is not an infinite regression.Fluffy said:Get a cake and cut it into thirds. You have just produced 3 infinitely recurring decimals in the real world (0.3^). To say that infinitely recurring decimals do not exist would be to say that mathematics is incorrect in the division of 1 by 3 and that therefore the process of division (and as a consequence multiplication, addition and subtraction) are all false.
A couple of problems here:michel said:This is the first I have seen of this thread; I can't see any justification for saying that 0.999999999 =1 - it isn't.
Just as a question, Fluffy, what would you do with "" ? Historically, mathematicians have tried to find the answer (which, of course, you know, there isn't one); I was always taught to use the fraction value as opposed to the decimal one.
I agree with what others have said; once 0.999999999=1, what about 0.99999998 ?........
What you are describing are known as asymptotes. They are usually first encountered when shown the graph of y=1/x. http://en.wikipedia.org/wiki/Asymptote See the second figure from the top.FervantGodSeeker said:Ugh...I hate math. Ok, correct me if I'm wrong, but I seem to remember that some graphs of certain equations have lines that "infinitely approach" a number, say 1. The line gets closer and closer to 1 (on either axis), but never actually reaches it. Isn't this basically the same thing?
Hey michel, I am uncertain if you are approximising when you say "0.9999999" but I just want to make sure that you understand that I am not talking about 0.9999999 but "0." followed by an infinite number of 9s (for which the mathematical notation is 0.9^)michel said:This is the first I have seen of this thread; I can't see any justification for saying that 0.999999999 =1 - it isn't.
Keeping the above in mind, it is impossible to have 0.9^8 because this would involve placing an 8 at the end of an infinite sequence of 9s. "at the end of infinity" is similar to ideas such as "outside of space" and "before time". It is certainly not a concept that is mathematically supported. Infinity has no end at which the 8 may be placed.michel said:I agree with what others have said; once 0.999999999=1, what about 0.99999998 ?........
Pi is one of the mathematical nuggets that I have not yet studied in depth. I understand it to be an irrational number (so it cannot be accurately written as a fraction). However, it is also a transcendental number and so it is part of an entire realm of mathematics I have yet to study. I am uncertain how you would go about calculating a transcendental number (the definition of one is sufficiently complex so I will not post it here) but as far as I am aware, it is not possible to write them without approximising.michel said:Just as a question, Fluffy, what would you do with "" ? Historically, mathematicians have tried to find the answer (which, of course, you know, there isn't one); I was always taught to use the fraction value as opposed to the decimal one.
Thank you but I was specifically after a reference that stated that 0.9^ is "a number approaching 1 that can never quite get there". Apologies for my skepticism but I do not believe that you will be able to find a respectable mathematician who will endorse that statement.Willamena said:
And a piece of cake is a fraction of the entire cake. It is 1/3 of the entire cake and 1/3 is an infinitely recurring decimal. That you have 3 pieces of cake makes sense since 3 x 1/3 = 3/3 = 1 and you have 1 cake.Willamena said:No, I have produced three pieces of cake. Three is not an infinite regression.
I agree but "I can't fly" does not equate to "flight is impossible" which appears to be analagous to what is being argued in that particular case.Willamena said:I can't = impossible.
That's exactly what it means.
Er, we don't use the decimal either... we use that fun symbol for pi =pSo, what's the fraction for pi?
There is always a form for them that does not use decimals. Wether you are talking about i or e... Theres some fun square roots that are irrational...I am very surprised. How do these mathematicians deal with numbers that cannot be written in the form m/n (that is to say that cannot be written as a fraction)? Only rational numbers can be written as fractions whilst all irrational numbers have to be noted using decimals (You can use surds for some but I don't think all irrational numbers can be written as a surd either).
heh, see the link from my above post... Its possible to write pi in an exact form... its just not the exact decimal form. The link above gives all the exact forms of pi...Pi is one of the mathematical nuggets that I have not yet studied in depth. I understand it to be an irrational number (so it cannot be accurately written as a fraction). However, it is also a transcendental number and so it is part of an entire realm of mathematics I have yet to study. I am uncertain how you would go about calculating a transcendental number (the definition of one is sufficiently complex so I will not post it here) but as far as I am aware, it is not possible to write them without approximising.
I hope you said this backwards... The fraction (ie the exact number) is always more accurate and most of the time easier to deal with than the decimal =p Espically now since computers are calculating more and more things for mathematicans... They can't compute a number after it is so big in decimal form (it ends up rounding at the end) so you alot of times do not get exact results. If you run the same equation on 3 different computers and they all get different answers its off to the pencil and paper method.However, the decimal to a sufficient degree will always be more accurate than the fraction. The fraction is useful for "simple" calculations in which relatively imprecise answers are sufficient (eg understanding the use and impact of Pi does not require an accurate output)
Sure, but that fun symbol is absolutely worthless anywhere outside of an equation. I would bet that anyone that needs to use pi (say, an engineer) will use the decimal version rather than a fractional version - knowing full well that it is an approximation. We know pi out to enough decimal points to fit within the tollerance of most any use that we need.Ryan2065 said:Er, we don't use the decimal either... we use that fun symbol for pi =p
I didn't see a single "exact form" of pi there. They all had elipses (...).Ryan2065 said:Its possible to write pi in an exact form... its just not the exact decimal form. The link above gives all the exact forms of pi...
I am a mathematician... I care about exact answers...SoyLeche said:Sure, but that fun symbol is absolutely worthless anywhere outside of an equation.
engineers do not care about exact answers... they care about answers close enough to what they need so whatever they make won't break.SoyLeche said:I would bet that anyone that needs to use pi (say, an engineer) will use the decimal version rather than a fractional version - knowing full well that it is an approximation.
But I can't see any mathematician using anything other than the symbol for pi even if we find the decimal form (that is if we find something that is repeating). It would be too long to write out.SoyLeche said:We know pi out to enough decimal points to fit within the tollerance of most any use that we need.
Sure we know the exact form... If we didn't then there would be many different versions (Everyones version of what pi should be) and the actual number wouldn't be able to be calculated.SoyLeche said:I didn't see a single "exact form" of pi there. They all had elipses (...).
I don't believe it is possible to write down exactly what pi is equal to, no matter what form you want to try.
But that's what having no initiating term means --the infinite series "0.9^" will never be complete and "1" is complete; therefore, 0.9^ can only ever approach 1.Fluffy said:Thank you but I was specifically after a reference that stated that 0.9^ is "a number approaching 1 that can never quite get there".
But I do not hold an "infinitely recurring decimal" in my hand, I hold one piece of cake in my hand. A whole piece. The infinite series that you profess to represent something "real" is in fact entirely conceptual.Fluffy said:And a piece of cake is a fraction of the entire cake. It is 1/3 of the entire cake and 1/3 is an infinitely recurring decimal. That you have 3 pieces of cake makes sense since 3 x 1/3 = 3/3 = 1 and you have 1 cake.
You haven't written what pi is equal to though. See those ...'s there? That's no more an exact representation than 3.14... is.Ryan2065 said:Sure we know the exact form... If we didn't then there would be many different versions (Everyones version of what pi should be) and the actual number wouldn't be able to be calculated.
Here is a nice looking equation for pi
Again, if it was not possible to write pi exactly in any form then we would not be able to compute it.
That is what pi is equal to... That pattern continues on forever... Its an exact representation =pSoyLeche said:You haven't written what pi is equal to though. See those ...'s there? That's no more an exact representation than 3.14... is.
Last I checked we aren't able to compute it. We've got pretty darn close approximations, but not exact.Ryan2065 said:Again, if it was not possible to write pi exactly in any form then we would not be able to compute it.
Which cannot be written. That's what I saidRyan2065 said:That is what pi is equal to... That pattern continues on forever...
The approximations are in decimal form... There are many forms of a number.SoyLeche said:Last I checked we aren't able to compute it. We've got pretty darn close approximations, but not exact.
It cannot be written in decimal form, but again, there are other forms of a number.SoyLeche said:Which cannot be written. That's what I said