That was an amazing read, thank you.
@lemmy.blahaj.zone
This looks great!
Bullet hell games are normally not my thing
It turns out genre doesn't have to do with one's preferences as much as the distribution of execution/planning/adaptation challenges:
https://xkcd.com/1251/ (there is always an xkcd about it)
FYI this comic is by https://stupidtwink.thecomicseries.com/. (also the creator of such internet sensations as "The weed that makes you gay" https://stupidtwink.thecomicseries.com/comics/173/)
https://piefed.blahaj.zone/comment/3791025
A near miss and a disaster are worlds apart in terms of consequence, but very close in terms of what went wrong.
May as well go through the proofs:
First, we need to establish that two infinities are equal in cardinality (aka size) if all their elements can be 1:1 mapped to each other.
So, to go from the reals within [0, 1] and [0, 2], we can multiply by 2. This maps every value within [0, 1] to every value within [0, 2], so these are of the same cardinality.
Where things get interesting is the proof that the reals within [0, 1] are of greater cardinality than every integer.
Say we have an arbitrary mapping from every integer to a real within [0, 1]:
0 -> 0.89236…
1 -> 0.47389…
2 -> 0.84776…
3 -> 0.18790…
4 -> 0.90542…
⋮ ⋱
This list contains every integer, but it does not contain every real number because we can always come up with a new one by ensuring at least one digit is different in each existing real:
0 -> …8… ≠ 9
1 -> …7… ≠ 8
2 -> …7… ≠ 8
3 -> …9… ≠ 0
4 -> …2… ≠ 3
⋮ ⋱
0.98803… is not within the list
Therefore, no 1:1 mapping between the integers and reals exists. Because the limiting factor is the amount of integers, the cardinality of the reals is greater than that of the integers.
Edit: https://en.wikipedia.org/wiki/Cantor's_diagonal_argument
You fool! I would recognized kwrite's "just edited" orange anywhere.
Which means... this "old lua script" isn't old at all and hasn't even been saved.
PREPARE TO BE GARBAGE COLLECTED IN RITUAL COMPETITIVE PAIR PROGRAMMING
The first one is incorrect, the limit doesn't exist unless you specify whether you're coming from the left or right.
On another note, I think their student has invented a new symbol for "Does Not Exist".
The opposite angles made by 2 intersecting lines must be equal, so we know that m/3 + 75 = m/2 + 64.
m/3 + 75 = m/2 + 64
-m/3 -m/3
75 = m/6 + 64
-64 -64
11 = m/6
×6 ×6
66 = m
thanks for using Leebra!
go to feed...