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Cake day: June 18th, 2023

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  • FTA:

    The big news this month is that “conveyor belts have unlocked the Y axis” in Terraria 1.4.5, meaning that you can now send items up and down along with using them to transport goods horizontally. Not only will that make them a lot easier to use generally, making it easier to navigate across long distances, but the demonstration also shows them hooked up to a chest, allowing you to instantly store all your transported items. That’s a massive convenience improvement, and will almost certainly lead to some fascinating new creations.








  • TastehWaffleZ@lemmy.worldtomemes@lemmy.worldThink about it
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    4 months ago

    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



  • 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.