Ste.D
@ste-d-1970.bsky.social
Software Engineer, Pool Player, Lurker
Consider b^x & x^b (for b>1)
When x=0, b^x > x^b (1>0)
When x=b, b^x = x^b
When x→∞, b^x > x^b
So graphs touch/cross at x=b
When b<e, graphs cross at/after x=b (b=2 crosses at 2 & 4)
When b>e, graphs cross before/at x=b (b=4 crosses at 2 & 4)
So π^x<x^π when x≲π
When x=0, b^x > x^b (1>0)
When x=b, b^x = x^b
When x→∞, b^x > x^b
So graphs touch/cross at x=b
When b<e, graphs cross at/after x=b (b=2 crosses at 2 & 4)
When b>e, graphs cross before/at x=b (b=4 crosses at 2 & 4)
So π^x<x^π when x≲π
November 20, 2025 at 11:15 AM
Consider b^x & x^b (for b>1)
When x=0, b^x > x^b (1>0)
When x=b, b^x = x^b
When x→∞, b^x > x^b
So graphs touch/cross at x=b
When b<e, graphs cross at/after x=b (b=2 crosses at 2 & 4)
When b>e, graphs cross before/at x=b (b=4 crosses at 2 & 4)
So π^x<x^π when x≲π
When x=0, b^x > x^b (1>0)
When x=b, b^x = x^b
When x→∞, b^x > x^b
So graphs touch/cross at x=b
When b<e, graphs cross at/after x=b (b=2 crosses at 2 & 4)
When b>e, graphs cross before/at x=b (b=4 crosses at 2 & 4)
So π^x<x^π when x≲π
$40 - players will win 60, win 20, lose 20 or lose 40
July 9, 2025 at 2:38 PM
$40 - players will win 60, win 20, lose 20 or lose 40
P(0aces):4/6*3/5=12/30
P(1ace):2/6*4/5+4/6*2/5=16/30
P(2aces):2/6*1/5=2/30
P(1ace):2/6*4/5+4/6*2/5=16/30
P(2aces):2/6*1/5=2/30
July 4, 2025 at 12:21 AM
P(0aces):4/6*3/5=12/30
P(1ace):2/6*4/5+4/6*2/5=16/30
P(2aces):2/6*1/5=2/30
P(1ace):2/6*4/5+4/6*2/5=16/30
P(2aces):2/6*1/5=2/30
(9/16) vs (1/16) => 90%
June 13, 2025 at 12:03 AM
(9/16) vs (1/16) => 90%
Although I’m happy that this continuously increasing percentage could reach 100, it seems like more justification is needed to prove it doesn’t approach some finite limit
March 25, 2025 at 1:00 AM
Although I’m happy that this continuously increasing percentage could reach 100, it seems like more justification is needed to prove it doesn’t approach some finite limit
Please add ability to refresh without losing place in timeline
March 11, 2025 at 1:28 AM
Please add ability to refresh without losing place in timeline