Originally posted by TheMaster37
divide 1 by 9 and your answer will be 0.111... Calculation is a strong proof 🙂 The division process will always go on, and will keep adding ones to the row. Therefore 1/9 = 0.111... (in wich the ... means that there are infinite ones behind the.) and multiplying both sides with 9 calculates the 1 = 0.999... Both are calculations, both with authorised op ...[text shortened]... en't equal). The complex numbers C don't have that, but you can take all the roots you want...
Thank you for taking the time to teach :-)
I will only make one last observation on this matter:
My thoughts on using calculation as definitive proof in this
case can cut both ways.
I dont belive 1/9 is any thing other than 0.111...
I just dont think you can prove it by testing it in calculus.
because for every extra decimal i calculate to prove it I can make a
multiplication to one extra decimal to refute it.
9/9 =1
1/9 =0.1 -> 9*0.1=0.9 (not 1)
1/9 =0.11 -> 9*0.11=0.99 (not 1)
1/9 =0.111 -> 9*0.111=0.999 (not 1)
1/9 =0.1111 -> 9*0.1111=0.9999 (not 1)
Unless you first prove 0.999... is 1 (that has been done here and I'm impressed and intrigued) you cannot prove that 1/9 is 0.111...
You can probably safetly assume the pattern will keep, but does calculating one more decimal acually prove it?
Again thank you all for the lesson. :-)