Dividing by a fraction is the same as flipping one it on its head and multiplying it.
0.25/0.5 is (1/4)/(1/2)
To multiply it we’d flip one, either works but for this example I decided to flip the second one: (1/4) * (2/1)
The top half of the fractions (numerators) multiply together, then the bottoms (denominators) multiply together. (1*2)/(4*1) = 2/4 which reduces to 1/2
THIS! THIS RIGHT HERE 💯🎉‼️
Your 1-1 relationship makes sense intuitively with a finite set but it breaks down with the mathematical concept of infinity. Here’s a good article explaining it, but DreamButt’s point of every set of countable infinite sets are equal holds true because you can map them. Take a set of all positive integers and a set of all positive, even integers. At first glance it seems like the second set is half as big right? But you can map them like this:
Set 1 | Set 2
1|2
2|4
3|6
4|8
5|10
6|12
If you added the numbers up on the two sets you would get 21 and 42 respectively. Set 2 isn’t bigger, the numbers just increased twice as fast because we had half as many to count. When you continue the series infinitely they’re the same size. The same applies for $1 vs $100 bills.
$1|$100
$2|$200
$3|$300
In this case the $1 bills are every integer while the $100 bills is the set of all 100’s instead of all even integers, but the same rule applies. Set two is increasing 100x faster but that’s because they’re skipping all the numbers in between.
The video in the linked article does just that. The page takes 5 seconds to load the video, the user changes the UA, they refresh the page and suddenly the video loads instantly. I would have liked to see them change the UA back to Firefox to prove it’s not some weird caching issue though
Yep. I use a piece of software that lets me drag components onto a stage and will auto generate code in the back end. We can then add our own code to customize the components.
I ran into a super cryptic error message while working on a time sensitive project and I was ripping my hair out trying to figure out what the hell was wrong. Turns out someone had pasted some code in from an email and the custom code editor displays the straight quotes and angles quotes exactly the same but the back end code generation fortunately displays them differently. The program didn’t like the character set for the quotes used in Outlook but didn’t give me the proper line number, the error made zero sense, and looking at the code didn’t show that anything was wrong.
IMO the worst part is that the dip looks like it’s salsa, not even cocktail sauce 😤