Yes. But 0.9999999 is entirely different than 0.999... (repeating) Why? Because as you so eloquently put it, 0.9999999 = 0.9999999 but 0.999... (repeating) = 1. There is no "debate" about this. Anyone who says otherwise is wrong. Period.
If there isn't an end where is the decimal point? The math that states that .3333...= 1/3 is flawed. It's an anomaly.
the math isnt flawed at all. clearly you havent even done 4th grade math yourself. otherwise you'd have proven to yourself that 1/3 = 0.3333....
But it doesn't, it just doesn't. There's a reason we have fractions instead of decimals. Fractions are exact, decimals are trying to rectify a problem. Fractions are exactly on, decimals are always a little bit off, no matter how many decimal points you push them to. Any math "expert" will tell you that. You will always be off when using a decimal that goes on and on. Decimals just aren't as accurate. No decimal value will ever yield you an exact fraction of a whole, it just won't, that's why they run forever. The fact that they have to go on forevever demonstrates the problem. The run on and on because they are not exact, and never will be. 1/3 =/= .3333... because they're operating at different levels of accuracy.
Fractions arent always accurate either. Wheres the fraction for Pi or trig functions? To be accurate things need to be in algorythmic form and shit. just shut the hell up. youre comepletely and utterly wrong. Every rational fraction can be 100% be put in as a decimal. .3 (with the bar over it) is 100% as exact as 1/3. There is no difference. As long as youre dividing by a rational number, youre always going to end up with a rational series of repeating or nonrepeating decimals.
there were 5 links posted, and most of them had something written by a phD in math. you think you know better than them?
do long division. divide 1 by 3, and tell me what you come up with. in fact, dont stop until the decimal stops. you will have proven me right before then. -the math is exact. which is why 1/3 = .3333... how else do you think they came up with '.3333....'? so stupid. reformat your hard drive, now.
The reson the decimal never stops is because it can't render the EXACT number. Dividing 27 by 3, that yields an exact number, it doesn't have to go on forever because 9 is EXACTLY one-third of 27. dividing one by three, will never yield the exact portion of the whole, which is why it goes on and on and on and on and on... Repeating decimals are not exact, they're a mathematical anomaly.
repeating decimals are exact. the only numbers that can't be accurately given in decimal form are numbers like pi, which have no end and dont repeat.
thats why they have the repeating notation, which then renders it completely accurate. Take 1/7 for example. its .142857 all repeating. Its completely accurate. You just cant comprehend the idea of infinity. and 27/3 does have infinate decimal places. they just happen to be zeros. Its the same as writing 9.0 with the zero repeating. we just dont notate that. doesnt mean its not there. the only anomalies in math i know of all involve dividing, multiplying and raising things to powers by infinity and zero. ie: 1/0, inifity^0, etc
which also cant be given in fractional form either. thats why i mentioned that all rational fractions have a decimal counterpart.
AMGRulz is wrong, but you don't know anything about math. First of all everything in math is built on axioms. Second of all, there are many problems that aren't solved and many things that aren't proven. It took 300 some years just for someone to prove fermat's last theorem.
And he definitely didn't do it with the method that fermat did. The methodology he used didn't exist when the theorem was first made.