20210617, 15:16  #2905  
Feb 2017
Nowhere
2^{4}·3·97 Posts 
Quote:
Quote:
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Last fiddled with by retina on 20210617 at 15:35 Reason: Remove URL tracking codes. You can do this yourself. 

20210623, 11:28  #2906 
"Mike"
Aug 2002
10000000101000_{2} Posts 

20210623, 16:00  #2908  
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
11^{2}·89 Posts 
Quote:
Now wondering whether it is correlated with ASD. Thanks for drawing my attention to this article. 

20210629, 14:55  #2909  
Feb 2017
Nowhere
2^{4}·3·97 Posts 
Observation of Gravitational Waves from Two Neutron Star–Black Hole Coalescences (Copypaste to a plainvanilla text file was not kind to the fancy formatting; I have improvised)
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20210709, 15:11  #2911 
"Mike"
Aug 2002
2^{3}×3×7^{3} Posts 

20210714, 00:52  #2912  
Apr 2012
Brady
2·193 Posts 
Quote:
As cases in point, consider jumping down a cliff with only a rope (no safety..and Alexander's spider men come to mind) to the bottom. You learn to trust your equipment and those around you. Some people just won't jump out of a perfectly good airplane no matter how good you tell them their parachute is. Others panic when at the bottom of a ten foot deep pool when told to take their mask and respirator off ..then put them back on after ten seconds. Never mind dive tables or all the other medical issues that can take place at a real depth doing more than taking in the scenery. My point is aptitude..you can lead a horse to water (maybe not a donkey though) but you can't make it drink. Kids are fun though and fart jokes always win..the stinkier the better. Last fiddled with by jwaltos on 20210714 at 00:58 

20210716, 19:35  #2913 
"Mike"
Aug 2002
20050_{8} Posts 

20210716, 20:24  #2914  
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
2A11_{16} Posts 
Quote:
There are (at least) a countably infinite ways of axiomatizing mathematics. Gödel proved this 90 years ago. One axiomatization includes the Continuum Hypothesis (CH) as an axiom. Another includes its negation, ~CH. Both can be proved to be consistent. The latest result appeals to those who find ~CH more attractive. Compare plane geometry and Euclid's axiom which states that there is precisely one line passing through a point and parallel to a line which does not pass through that line. Each of the axioms which replace "precisely one" with "precisely zero" or "an infinite number of" generate consistent geometries  spherical geometry and hyperbolic geometry respectively. All three are useful in practice. 

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