Quote:
Originally Posted by N0B0DY  I agree, Lloyd, but mathematicians don't agree with each other and I wanted to know if there is presently a leaning to one side or the other.
Some of the arguments are as follows:
"In mathematics, the recurring decimal 0.999… , denotes a real number equal to 1. In other words, "0.999…" represents the same number as the symbol "1". The equality has long been accepted by professional mathematicians and taught in textbooks. Various proofs of this identity have been formulated with varying rigour, preferred development of the real numbers, background assumptions, historical context, and target audience." http://en.wikipedia.org/wiki/.999 |
When I viewed the link
http://en.wikipedia.org/wiki/.999 . The first and the whole paragraph really states exactly as what was quoted above.
However, the last paragraph (as a conclusion) in that web page states that "Number systems in which 0.999… is strictly
less than 1 can be constructed, but only outside the standard
real number system which is used in elementary mathematics."
Sorry to point out that the wikipedia page concludes that "0.999… is strictly
less than 1 can be constructed (despite only outside standard real number system or outside elementary mathematics).
I also don't understand the following operations.
If 0.999... = 1 , then after exchanging the left & the right hand side, 1 = 0.999... .
When both side divided by 1, then it comes out 1/1 = 0.999.../1 , then the right hand side = 0.999... ,
however, normally, 1/1 or 2/2 or n/n all simply = 1, not 0.999... .
Best Regards. Bottomlander