A question of numbers (one for the maths fans)

Yes it does. Ever heard of irrational numbers? practical purposes are completely besides the point. we are talking about pure math here.

that would depend on how you define your infinite line and on how fast you are traveling. there are ways of making a one to one correspondence from every point in an line to every point (but one) in a circle of any size.

RR,I had heard that Pythagoras was so upset with irrational numbers that he pledge his students to secrecy but I'm not sure about this story: Yes, the incommensurateness of the rationals and irrationals is a puzzling even counter intuitive finding. Let say you have a line length of 1 and another line length of pi. It seems like you could find a small enough length that would evenly measure both of them. Pi would have three something times as many of those tiny lengths than would the line of 1, but no way. It can't be done. There is no length however tiny that can be used to evenly measure the two lines.Here is a simple proof by contradiction (I believe that is what it's called. It's been quite a while since I've done math) They are called irrational numbers because they can't be expressed as the RATIO of two integers: .3333 is 1/3 but pi is not a repeating decimal. The decimal is only getting closer and closer to pi. It will never equal pi.I still find this a strange thing about everyday life. Incommensurability is a mystery to me. It is one of many hints that reality is not what I think it is.lfen

Yet it is a real ratio which real calculations can be performed on, without the need to approximate. It seems like you are rejecting a great swathe of mathematics.e^Πi+1=0 springs to mind. We cannot say this is true by your definitions. Likewise we know that Π = ^c⁄_d, but now you are proposing that^(Πd)⁄_c ≠ 1It's fine if you want to reject any number you cannot write down - but you need to appreciate just how that might affect the rest of maths.Incidentally, if it suits you to think in terms of approximation, then you know that if you made any approximation of 0.9999.... it becomes 1. If you don't like the decimal representation of an infinite geometric series, you can think of it in terms of fractions - it's just more difficult to write and less likely that people will understand the number being represented. It is strange that every decimal number has different ways of being represented - even though we accept it as common for fractions.

Rat,Take a look at this wikipedia article:
Zeno's paradoxes - Wikipedia You are having the same problem Zeno had. He proved that Achilles could never catch up to a tortoise because in order to catchup he would have to first go half way. Once there he would have to go half of the next distance and then half of that and he would always be some fraction of the distance behind the tortoise.This brilliant (but ultimately fallacious proof) demonstrates something we know not to be the case. But if I recall correctly the mathematics to handle this were developed much later by Newton and Leibniz..999... is shorthand for an infinit sum .9+.09+.009+ ... and calculus has proved that the value of the sum is 1.It's good to think about these things but naive assumptions can be false. There are some good books on mathematics written in a popular style. Why not read one?lfenABE: Here is another link to a overall math view of this:
http://www.andrews.edu/~calkins/math/webtexts/numb13.htmEdited by lfen, : see ABE above

e^iΠ+1=0 please Though could this be the first mention of Euler's Identity at EvC? Hmmm, and 100 posts in and I don't think anyone has advanced beyond this yet

I hope not, but I can't be sure. It would seem a great angle for the fine-tuners to try and come from. Unfortunately, it's not like its an easy thing to search for! Come one, we've moved at least a little bit! If you fancy trying to mathematically prove something to somebody in this medium, go for it. I'm sure it'll be as entertaining as usual. I considered starting calculus 101 in light of rRs infinity issues.

Yes, but the direction matters It's not the typesetting, it's teaching formal mathematics to an engineer pearls before swine, teaching pigs to sing, etc

What the...What are you smoking, Riverrat?

Give him some slack, it's a damn site shorter proof than Godel's

Zeno's problem is that he assumes that man runs like the graph of a square root, or maybe more precisely, runs like the value e

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All a man's knowledge comes from his experiences

RiVeRrat Let us go through this againWe are subtracting the infinite quantity 0.999... from 9.999... ok?Since the quantity that is being subtracted is to the right of the decimal point then we have the following operation..999... minus .999...These 2 quantities, though infinite, are equal since the same number repeats itself and there is a one to one correspondence among all the member of the sequence. Therefore, it follows logically, since subtracting ANY given quantity from that same quantity equals zero.Another way to look at it is this. We know that
.9 is .1 in difference from the value of 1
.99 is .01 in difference from the value of 1
.999 is .001 in difference from the value of 1
.9999 is .0001 in difference from the value of 1Now to illustrate the concept let us make a table of values

Given Value               Difference from 1          Proof
​
.9                         .1                  .9+.1=1
.99                        .01                 .99+.01=1
.999                       .001                .999+.001=1
.9999                      .0001               .9999+.0001=1
.99999                     .00001              .99999+.00001=1
.999999                    .000001             .999999+.000001=1
.9999999                   .0000001            .9999999+.0000001=1
.99999999                  .00000001           .99999999+.00000001=1
.999999999                 .000000001          .999999999+.000000001=1

.999... + 0 = 1 is correct because,since it continues off into infinty,it cannot ever show a difference value that can be added to it in order to arrive at one. No difference value is the same as zero difference value.Now if I had graphing capabilty or if I were better versed in calculus and the concept of limit then I caould show you how the quantity shrinks to zero in the approach to the infinite value.Edited by AdminJar, : formatting

The number 0.99999... is defined as an infinite series.If you accept that the number exists, you must accept the concept of infinity.You are of course free to refuse this, but this would have fundemental effects on a lot of other things.When youaccept the notation 0.9999... you accept that the concept is that the 9's are repeated an infinite number of times.Now if you accept this or 0.9999... and 9.9999... then you must accept that
9.9999...-0.9999... =9 is meaningfulInstead of placing nine an infinite numbr of times, you subtract an infinite number of nines.One way to prove that 0.9999... equals 1 is to use infinite series.0.9999... is defined as the sum9/10 + 9/100 + 9/1000 + ...Does this sum converge on a number?The difference from 1 is 0.1 in the first instance, then 0.01, then 0.001 etc, the difference i 1/(10^n) in the n'th instance.Now if 1 does not equal 0.9999... then 1-0.9999... must be some number different than 0. Assume that 1 does not equal 0.9999... , then there must be difference, lets call it d, between them, that is
1-0.9999...=d, where d>0Now we know that the difference between 1 and 0.9999... is 1/(10^n) in after n instances.But we can make n arbitrarely large, since the sum that makes u 0.9999... is an infinete series, but then there will be a number N where 1/(10^N) is smaller than d!But that is contrary to our claim that d>0, so we can conlude that d=0, that is 0.9999...=1!This all hinges on the fact that 0.9999... is a sum of infinite many addends, so if you accept the notation 0.9999..., yuo must accept the conclusion that it equals 1.

I object both, but accept both.Can you get .999... by multiplying 2 numbers?

On my Ti-86, a number with twelve decimal places is assumed to go on for inifinity. So .999999999999 stretches on for infinity, as should pi (but my calculator stops at eleven for some reason).Anywho, .999999999999 / 2 = .5. So, .5 *2 = 1 or .999999999999again, my calculator considers 12 decimal places to strech for infinity, so I have twelve for the decimals here (except .5, of course)

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All a man's knowledge comes from his experiences