Re: Problems I have with 1.999...=2

Kirby Cook <kwmcook@xxxxxxxxxxx> wrote:
: Problems I have with 1.999...=2

First problem, what do you mean by 1.999... ?

Is it a number? Numbers do not move. They do not "approach"
anything. Every number has a fixed value that never changes.

If you do not think it is a number, then clearly 1.999... does
not equal 2.

If you think is is a number, what number do you think it is?
Remember, if it is a number, it is not approaching anything.
It is definitely not approaching 2. 2-1.999.... has a value
that never changes. What do you suppose it is?


: Commonly, the first "proof" or demonstration offered involves setting
: .999... =x, multiplying .999... by 10, subtracting x from 10x, and
: asserting that 9x=9. Taking that step by step, if x=.9 and 10x=9,
: 9x=8.1. When x=.99 and 10x=9.9, 9x=8.91. Lining up the first few examples,
: 10x 9 9.9 9.99 9.999
: -x -.9 -.99 -.999 -.9999
: 9x 8.1 8.91 8.991 8.9991

: So, even if you claim leave to ignore the convention that multiplying a
: number by ten always adds a zero to the end of the number by arguing
: that there is no "end" to .999... (a dubious dodge in itself, IMO), if
: you let those two numbers, x and 10x march out to "without limit" in
: lockstep, the upper 9 will always be one step to the left of the lower,
: and 10x-x will never equal 9.

: The flaw in the oft-cited second "proof", or demostration, which tries
: to show that there is no number between 1.999... and 2, may be found in
: the law of the reciprocal, by analogy and inference. Say, for instance,
: that there is no number between the infinite sum (difference) 1-.999...
: and zero.Taking it step by step, 1-.9 has a reciprocal of 1/(1-.9) or
: 10; 1-.99 has a recirpocal of 100, and so on. So, if you assert that
: there is no number between 1-.999... and zero, then you are also
: asserting that there is no number between 1000... and a point often
: termed the point at infinity. And how many of you will buy that?

1000... is not a number. Neither is infinity. No number
exists between non-numbers.

: It should be obvious, I hope, that I am directing my remarks not to
: those who carefully assert that 1.999... =2 is merely sloppy shorthand
: for the idea that 1.999... *approaches* 2. No, my remarks are for those
: hopelessly superstitious minds that claim that "equals means equals" in
: this case.

1.999... does not approach anything. It is hopelessly
superstitious to believe that numbers move. Is 999 approaching
1000? If we wait a few years, will 999 be any closer to 1000?
Why would 1.999... be on the move but not 999?

Learn some math.

Stephen
.

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