My question is if there are other transcendental numbers that can be used in an exponent that can give a integer number other than eulers number to the power of a log. Since a log is pretty much an inverse function of e to an exponent I feel like it’s kind of like cheating to get an integer. (Although what if there was an inverse function of pi that you could use to get an integer?)
I believe in whatever I want to believe and that's all I care about. It makes things very simple because then I neither have to argue or explain myself.
Everyone missed the obvious solution. One on top spanning the corners of the four original final blocks. The number is corrected and the original design is retained.
Rewatching this today after someone in the mealroom at work suckered me into helping them with a 1060 piece puzzle that turned out to be a 1040 piece puzzle.
They're imagining infinity as a sequence iterating in real time. If one pile has an extra bill, then the other must. So on. Infinity isn't a number though.
My guess is: the average number of jumps is 3.66 (and the most common number of jumps is 3 - which occurs 21.60% of the time, compared to 20.16% for 4 jumps). admittedly, I am 4 years late to this party, but if anyone got a similar result, let me know. I love math, but I expect my calculations are probably wrong. 😄
When Mat(hs) P. said fractions can be ordered I flinched. I didn't realize in English we do a distinction between fractions and decimals. In my country we are thought that decimals are a type of fraction. Fractions are translated as дроби (droobi) and decimals are deseti (tenth) or stotitsi (hundreth) etc. Perhaps it is only me, but I have always used drobi for both.
$20 infinity is just a denser $1 infinity, but their values are still the same. Imagine a m³ of steel and a m³ of feathers. Vastly different densities, but they still have the same volume. A m³ of steel is just as big as a m³ of feathers.
Okay, but the point of an infinite pile of money is you probably want to spend it. And you probably want to spend it on something big before the government finds out about your inflation-causing, economy-crashing piles of cash. Instead of comparing the count of things in the pile, I want the pile that requires the least amount of withdrawals to pay for my super yacht.
The amount of money in the two stacks is different. The number of pieces of paper is the same - there's a one to one correspondence between the two sets. But the pieces of paper have different values so the total value is not the same.
I was recently made aware that you can technically program at least one simple game in Excel, and now I'm wondering what the limit of that is, but don't have the skills nor time to dedicate to answering that question.
It's a thousand years in the future! People will probably be able to fold spacetime in on itself, make the last block the size of the solar system, and levitate it above the rest--they'll figure something out.
It is absolutely hilarious to me that you turned up to a solar eclipse and (from the perspective of everyone else that was there) you turned up with a dodgy homemade telescope and then POINTED IT THE WRONG WAY.
The thing that had really got me going, was that when they decide by infinity, it will come out as non-applicable or NaN, but then again, we definitely know that if you had an infinite number of 50 dollar bills, to one dollar bills, it would always equal infinity. I was thinking not long ago, if an exponential downward graph was going to infinity (say dividing x by 2 for every number) would it still be possible to equate that to infinity? I know that exponential goes for infinity, but if it were to be dividing itself by 2 or 4, would you be infinitely be dividing the number, or would the number be infinite?
