does 0.9999999.......... equal 1

Thanks for the debate Con. Con spent much of his effort on one of my proofs. He basically left the other two untouched. Nice! Let's end this. *Maths Argument #1*I had indicated that 1 divided by 3 is indistinguishable from 0.999. .. divided by 3 and this was confirmed and conceded by Con. In round 2, Con concedes:"the answer that satisfies 1 divided by 3. .. when you multiply it by 3, you get 0.999. .. "My response:This is a concession that dividing 1 by 3 and dividing 0.999. .. by 3 are indistinguishable and *this* alone shows that 0.999. .. is equal to 1. The same three things that make 1 also make 0.999. .. Conceded. Con continues:"1 is not an incorrect value. ..1 is technically made up of 3 incorrect values. That doesn't mean 1 is an incorrect value. "My response:Ok, this bit here, along with Con's concession that 1/3 = 0.999. .. /3 has Con's logic indicating that 0.999. .. is NOT an incorrect value as he tried to claim before. Con says that while 1 is made up of 3 "incorrect values," 1 is not an "incorrect value," but the number 0.999. .. is made up of THE EXACT SAME 3 "incorrect values" and Con somehow still claims that that 0.999. .. is an "incorrect value. "Even though Con never explained what an incorrect value is, by Con's own logic, 0.999. .. is NOT an incorrect value because it's made of 3 incorrect values IDENTICAL to the 3 incorrect values that make up the number 1. *Maths Argument #2*I had indicated that 1 - 0.999. .. = 0.000. .. because without and END to the 9s in the decimal being subtracted from 1, there is no END to the 0s in the answer's decimal thereby equaling 0, because 0.000. .. = 0. Con concedes:"1-0.999. .. does not equal 0. it equals 0.0000000. .. .1. There is still a 1 at the end of it. But it is being pushed back by infinitely many nines. "My response:So the response to me indicating NO END to the 0s in the answer's decimal because there's no end to the 9's in the decimal being subtracted from 1 is just Con conceding that there is NO END to the 9s? I view this as a concession that the answer to 1 - 0.999. .. = 0.000. .. WITHOUT END. Conceded. *Maths Argument #3*I mean, this is really where Con focused their efforts, and honestly, given the lack of a refute to the other maths arguments, I could just leave this one alone and still net the win, but I'm obnoxious. I had indicated that since multiplying 0.999. .. by 10 was the exact same thing as adding 9 to 0.999. .. that algebraically 1 is indistinguishable from 0.999. .. So Con indicated that doing this algebraic exercise with . ..999.0, the infinite string of 9s going to the left instead of the right of the decimal. indicates that . ..999.0 = -1. Con also points out that putting the infinite string of 9s in both directions would then equal 0. To me, this doesn't take away from the fact that algebraically 0.999. .. is indistinguishable from 1, in fact, though counter-intuitive and seemingly paradoxical, if 0.999. .. does in fact = 1, then it follows that the other direction of infinite 9s could be accomplished by making that value -1 and if you were to put . ..999.0 and 0.999. .. i. e. (-1 and 1) you should get 0. Con asks:"Honestly, do you believe that . .. .999999=-1"My response:Sure. If I say yes to this question, does it negate that 0.999. .. = 1? Nope. Both can be true, and are. Con continues:"the equation is paradoxical because it would seem to prove that multiplying a positive number by 10 results in that number minus 9. "My response:Great. This doesn't take away from the point that 1 and 0.999. .. are algebraically indistinguishable, it just shows that other counter-intuitive results can arise from algebra. .. that's it. If anything it's a knock on algebra, not 0.999. .. = 1. *Conclusion*0.999. .. = 1 because of the untouched reasons #1 and #2 and for the irrelevant algebraic paradox Con attempts for #3. Opt-in voters, take note.