While I appreciate the effort the author has clearly put in here, Im not sure the visualization provides much in the way of practical intuition. These seem to essentially be mechanistic explanations of the rote bits of matrix math.
There are already rich geometric interpretations which provide useful intuition for that generalizes, rather than just demonstrating mechanical details.
Used it for like a year before switching to opensuse tumbleweed. For rolling release Ive found it to be a lot more stable, though some of more obscure packages I use are harder to obtain.
Classic problem of trying to draw definitive lines between these things. I would guess this is more motivated by the social aspects of academics today than any real issue.
In any event reading the work of philosophers has certainly made me a better thinker and mathematician. Without a broad base of thought one can easily get sucked into many intellectual traps and tar pits. In my case, I found Penelope Maddy and Wittgenstein to be helpful when I was figuring out what math "is".
Ah, I think I see. Open sets are just how we encode information topologically. Theyre sort of the "atoms" of topology; the types of opens sets you have say how the topology behaves.
In particular open sets are neighborhoods of all of the points they contain. This means they contain all the topological information about all of their points.
Closed sets are not neighborhoods of their points in general. Eg [0,1] contains no neighborhood of 0 or 1. Then we would require knowledge of the space around those points to know how a function behaves just on [0,1].
In standard calculus this amounts to "taking the left and right limits".
Fuji XEs are nice, small, relatively cheap bodies with interchangeable lenses. If youre looking for something small and know how to (or are willing to learn to) use a camera, thats what I recommend.
If portability is not a concern, you can pick up used high end Nikon DSLRs and F mount lenses very cheaply right now. Nikon is going all in on mirrorless now so this stuff is "last gen" hence cheap.
Otherwise, just avoid Canon. Theyre becoming increaingly scummy and you probably dont wanna get caught locked into their system.
I got a tiny Fuji mirrorless for my "best camera is the one with you" checkbox too. Next time I catch gear acquisition fever though, I might have to get one of those little Ricohs.
The optics depend so much on physical size that phones have to fake this stuff.
Idk why apple doesnt just cut the crap and just release like a m43 with swappable glass rather than all this silly multiple sensor stuff.
Im surprised by all the folks who always pop into these threads saying theyve replaced their XXXX-expensive-dedicated-camera with their phone.
Outside of wide DoF, wide FoV, well lit shots I find my camera and iphone to be pretty incomparable.
If apple starts letting us swap the glass out one day we might be have a fight but currently I just dont see it being one at all.
Yeah Im unsure what the point is. The motivation for CT in programming seems weak.
Eg Stuff about types and endofunctors feels like trivial examples using the jargon just to use it. OTOH discovering the Top->Grp functor in algebraic topology is kind of unexpected and revealing.
Eating super spicy food definitely leaves me feeling kind of drunk.
Have met others who have this and others who doesnt believe me/think Im exaggerating.