20191106, 22:16  #12 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×3×5^{2}×73 Posts 

20191107, 00:51  #13  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2×5^{2}×43 Posts 
Quote:
https://www.wolframalpha.com/input/?..._19+to+decimal ETA: Oops, got the 1's in the wrong base. But at least I learned something: An odd number of 1's in an odd base will never evaluate to an even number, regardless of any 0's present anywhere. Last fiddled with by a1call on 20191107 at 01:18 

20191107, 01:37  #14 
Feb 2017
Nowhere
2·47·53 Posts 
Maybe, but retina specified 2_{10}, not "1.999999999... in decimal."
You have to invoke limits to say they're "the same." In any case, it doesn't answer my question  what's the conversion algorithm? It can reasonably be argued that using .999999999... in decimal, or .1111111... in binary to express an integer isn't algorithmic because the decimal or binary expansions do not terminate, so they can not express an integer exactly using a finite number of arithmetic operations with integers. 
20191107, 02:14  #15 
6809 > 6502
"""""""""""""""""""
Aug 2003
101Γ103 Posts
3^{2}×11×101 Posts 
2_{10} = the following in binary

20191107, 03:42  #16  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6280_{10} Posts 
Quote:
I start with 1_{2} and convert to base 10 to get 1_{10}. Too small. Then I try 1.1_{2} and convert to base 10 to get 1.5_{10}. Too small. Then I try 1.11_{2} and convert to base 10 to get 1.75_{10}. Too small. Then I try 1.111_{2} and convert to base 10 to get 1.875_{10}. Too small. Then I try 1.1111_{2} and convert to base 10 to get 1.9375_{10}. Too small. ... <repeat β times> ... Then I try 1.1111...._{2} and convert to base 10 to get 2_{10}. Yay. Found it. 

20191107, 04:06  #17 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2150_{10} Posts 
Decimal 2 is a defined mathematical quantity.
1.11..._{2} is not a defined mathematical quantity so it can not be equal to 2. This is despite the fact that the limit of the sum 1+1/2+1/4+... converges to 2 as the number of addends approaches Infinity (an undefined quantity). Last fiddled with by a1call on 20191107 at 04:07 
20191107, 04:21  #18 
Jun 2003
19·271 Posts 

20191107, 04:35  #19 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{3}·5·157 Posts 

20191107, 04:41  #20  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{3}·5·157 Posts 
Oh, WP has an article about it.
https://en.wikipedia.org/wiki/0.999... Quote:


20191107, 22:25  #21 
6809 > 6502
"""""""""""""""""""
Aug 2003
101Γ103 Posts
3^{2}·11·101 Posts 
Mod note:
Timekeeping posts split off to this thread: https://www.mersenneforum.org/showthread.php?t=24923 This the post that started it and refers to the prior posts in this thread: Last fiddled with by Uncwilly on 20191107 at 22:25 
20200705, 03:54  #22  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3·41·47 Posts 
Quote:
Buy a loaf (1), + if (they have any eggs) get 12 (loaves). 1+12=13. Last fiddled with by kriesel on 20200705 at 03:54 

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