Originally posted by jxyama
who says 1.99999... is not a rational number? 0.1111... is a rational number because it's 1/9. so it's 1 + 9*0.1111..., sounds perfectly rational to me.
Exactly.
Originally posted by jxyama
who says 1.99999... is not a rational number? 0.1111... is a rational number because it's 1/9. so it's 1 + 9*0.1111..., sounds perfectly rational to me.
Originally posted by jxyama
math is kinda convoluted... it's been a while since i've had to think about this stuff. (i majored in math in college, but that was more than 5 years ago.) any active mathematicians out there?
Originally posted by jxyama
exactly. so 1.999... may not look like "2" that we are used to but it's equal to two. the symbol "2" is perhaps too crude to adaquately describe all the properties of the number "two"?
math can't change its definitions... either 1.999... is equal to 2 or it is not. "equivalent" doesn't really make much sense. what does it mean? it's equal sometimes, but not all the time? that's too ambiguous for math...
who says 1.99999... is not a rational number? 0.1111... is a rational number because it's 1/9. so it's 1 + 9*0.1111..., sounds perfectly rational to me.
Originally posted by zapp
It looks cool though and did get my rather slow brain working again. Thanks, Now to ponder the meaning of life.
Originally posted by zapp
You are right
1.99.. does equal 2
1.99.. = 1.99..
1.99.. = 1+ .99..
1.99.. = 1 + 9 * .11..
1.99.. = 1 + 9 * 1/9
1.99.. = 1 + 1
1.99.. = 2
Originally posted by zapp
You are right
1.99.. does equal 2
1.99.. = 1.99..
1.99.. = 1+ .99..
1.99.. = 1 + 9 * .11..
1.99.. = 1 + 9 * 1/9
1.99.. = 1 + 1
1.99.. = 2
Originally posted by Dros
That is nicely put. I agree .111... = 1/9, but does .999... = 9 * .111...? Is that an appropriate operation on an infinitely long decimal?
Originally posted by kevin49093
But you can't divide by zero!
Originally posted by sjjordan
I'm having a great discussion with a friend about the following...
1. if x=1.999...infinity, then 10x=19.999...infinity. Subtracting 10x from x gives 9x=18. Dividing both sides results in x=2.
2. Using your calculators on this one. 1/9=0.111...?. 2/9=0.222....?. 3/9=0.333...?. 4,5,6,7,8 follow the same pattern. What, then is 9/9? It is 0.999...infinity.
Do you think those are valid? I think they are and thinking in infinite terms 1.999...infinity is equal to 2.
My friend thinks he can add any number to infinity because he just can.
Food for thought. Any you want to add?
Originally posted by zapp
You are right
1.99.. does equal 2
1.99.. = 1.99..
1.99.. = 1+ .99..
1.99.. = 1 + 9 * .11..
1.99.. = 1 + 9 * 1/9
1.99.. = 1 + 1
1.99.. = 2
johnnowak said:You clearly cannot replace .9999... with 1.
I hope this ends the discussion.
Doctor Q said:I add my confirmation to those above. Yes, .999... is exactly the same number as 1. They are two notations for the same value, just as all of these are notations for the number 13:
13
15 (base 8)
XIII
9+4
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Powerbook G5 said:I did a science fair project on the particle-wave theory of light. I had a pretty nifty demonstration with flashlights, a cookie sheet, and a cardboard box with a few holes cut into it. Funny thing was, I just did it to be lazy since it was such an easy project and I hated doing science fair stuff and it somehow impressed my teacher and I got stuck going to the state science fair and wasting 5 days bored out of my mind.