20191106, 22:16  #12 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
11,317 Posts 

20191107, 00:51  #13  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2,243 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
169A_{16} 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
101ร103 Posts
2×11×479 Posts 
2_{10} = the following in binary

20191107, 03:42  #16  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2×3,229 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 โ 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
2,243 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
5·29·37 Posts 

20191107, 04:35  #19 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
193A_{16} Posts 

20191107, 04:41  #20  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2·3,229 Posts 
Oh, WP has an article about it.
https://en.wikipedia.org/wiki/0.999... Quote:


20191107, 22:25  #21 
6809 > 6502
"""""""""""""""""""
Aug 2003
101ร103 Posts
2×11×479 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
2·17·191 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 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Smallest 10^179+c Brilliant Number (p90 * p90)  2147483647  Factoring  49  20210818 07:41 
Could a Distributed Computing approach help find the smallest Brier number?  jasong  Math  5  20070529 13:30 
smallest number used in a mathematical proof?  ixfd64  Lounge  22  20060201 17:06 
Can you find the smallest number?  Fusion_power  Puzzles  8  20031118 19:36 
Smallest untested number?  wirthi  Math  10  20031005 13:02 