A question of numbers (one for the maths fans)

RiveRrat x= 0.999... 10x shifts the decimal place one value to the right so this equals 9.999... We need not concern ourselves with the infinity aspect of the values to the right of the decimal since all we need to know is that they are equal to one anotherLogically you can since both sides of the equation{after the decimal point} are infinite numbers and they are of equal value
.999... = .999... so subtracting equals from each other results in zero
Hence the only way for the equation to balance is for 10x to equal 9.999... and .999... to equal 1 QED

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Dear Mrs Chown, Ignore your son's attempts to teach you physics. Physics isn't the most important thing. Love is.Best wishes, Richard Feynman.

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

riVeRrat You are asking what happens to the last digit in an infinite series? Have you not heard what has been said? Infinite means no last digit.I am assuming you missed post 102 where I gave a clear explanation {I hope!} so I will ask you to review it and see if it helps clarify.The number is rational and is less of a problem mathematically than a number you are likely familiar with called Pi. You are aware that it is the ratio of a a circle circumference to its daimeter.Are you aware that it is a non-reapeating infinite number? Do you question the reality of it as well?

riVeRrat You are close RR but you need to take that last step. Remember that the number .999... as an infinite series is simply a repetion of the same number over and over. Each 9 in the series has a corresponding 9 being subtracted. Since both are infinite they are the same size and thus we are simply subtracting a number {though infinite} from exactly the same number.
Since numbers are simply symbols representing an agreed upon value we can easily introduce the symbol ∞ for infinity,set it as equivalent to .999..., and proceed with subtraction and we get ∞ - ∞ = 0. Edited by sidelined, : Edit for clarification

riVeRratRecurring but finite.