What are some proof tools that you use very frequently?

I don't mean contradiction, induction, etc. Rather, more granular techniques that keep coming up again and again. I also don't mean famous results per-se, unless they are themselves common stepping stones to other results.

I know this is a bit of a silly question to ask because it's hard to set the threshold beyond which something becomes a legitimate technique. Obviously deriving bounds on a quantity is too generic to qualify, but on the other end there's some very niche stuff that not too many people might find useful.

I guess the goal here is a little toolbox, if you will, of tools that you find yourself using repeatedly, and that might be useful to a broad audience.

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u/ObliviousRounding — 19 hours ago

To what extent was math as we know it today inevitable?

I'm not a mathematician by training (engineer) but I'm endlessly fascinated with the discipline. I keep hacking away at books on real analysis, functional analysis (plus convex analysis for my optimization stuff), measure theory and sometimes abstract algebra. It's incredibly hard self-learning this stuff patchwork, but it's rewarding on the rare occasion that something sticks.

Recently while trying to sus out the differences between closedness, completeness, compactness, etc for the umpteenth time, I ran into this historical paper on the origins of compactness. It was fascinating seeing all these names and dates mentioned in one place. It made the whole thing seem slightly less mythical and more, er, human.

It also taught me that there were, in a sense, competing definitions of similar concepts, and some won out eventually. This got me wondering: was the development of math as we know it today inevitable, or could it have gone a completely different way? In my mind, this contrasts sharply with the idea that math formalizes certain fundamental truths about nature.

Thoughts appreciated!

u/ObliviousRounding — 6 days ago

Levoit Core 300: Is it normal for the area around the device to be dusty all the time?

I'm so confused by this device. I have it next to a laptop placed on the same surface if that matters. The air purifier is on all the time. Just changed the filter. The surface of the table is *always* full of dust especially around the device. My laptop screen is also always dusty. Sometimes I'd switch the air purifier off and it would seem to me that *less* dust accumulates on the laptop screen.

Is any of this expected? What am I doing wrong?

reddit.com
u/ObliviousRounding — 6 days ago

Levoit Core 300: Is it normal for the area around the device to be dusty all the time?

I'm so confused by this device. I have it next to a laptop placed on the same surface if that matters. The air purifier is on all the time. Just changed the filter. The surface of the table is always full of dust especially around the device. My laptop screen is also always dusty. Sometimes I'd switch the air purifier off and it would seem to me that less dust accumulates on the laptop screen.

Is any of this expected? What am I doing wrong?

reddit.com
u/ObliviousRounding — 7 days ago

Not Carell, not Gandolfini, not anyone else

Graham as Lorelai is the most born-to-play-this-role role ever. Nobody has ever killed in a role as much she killed here.

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u/ObliviousRounding — 9 days ago

Cautionary Tales (Tim Harford): Are the episides getting weaker?

I'm a big Tm Harford fan and this is by far my favorite podcast, which is why it pains me that the episodes feel like they're getting less substantial and more fluffy and drawn out. Is the weekly schedule too tight? I think I'd be OK with going back to one regular episode every other week interlaced with a conversation every other week, even though the conversation isn't my favorite format, if it means maintaining a high standard of quality.

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u/ObliviousRounding — 24 days ago
▲ 2 r/IKEA

JALL hamper

Needed more of these, but when I went to get them they seemed distinctly smaller than the ones I owned. I looked it up: they used to be 70L; the current ones are just 50L. So the older ones are 40%(!) bigger.

It's not going to ruin my life or anything but it's pretty annoying how this keeps happening.

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u/ObliviousRounding — 28 days ago
▲ 41 r/IKEA

Got this today for 8 bucks. Doesn't fit in any of my bathrooms, doesn't work anywhere else, but couldn't afford not to take it.

Pretty shelf too.

u/ObliviousRounding — 1 month ago
▲ 1.0k r/theocho+4 crossposts

TIL there is a an artistic cycling World Cup (Swiss athletes Larissa Tanner and Simona Lucca)

u/H2Ospecialist — 1 month ago

Prediction: Marotta and Ausilio will leave within 12 months unless ownership changes

It feels like a weird dynamic is slowly emerging. It's almost like the rich English clubs have outsourced the scouting role to clubs like us knowing that they can hijack any deal with their financial power.

Marotta and Ausilio now face a literally thankless job. No matter how good of a job they do, they are between the rock of stingy owners who sabotage them at every stage, and the hard place of the thankless fans who don't understand what's going on and keep blaming them for these transfer failures.

If I were them, I would hardly see any value or fulfillment in this job beyond loyalty to Italian football. If or when that fizzles out, it only makes sense that they leave to a place that values their work, backs them with money and pays them appropriately.

I unfortunately see dark clouds ahead for us unless we get different owners.

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u/ObliviousRounding — 1 month ago
▲ 343 r/LiveFromNewYork+2 crossposts

The many loves of Dobie Gillis( 1959 - 1963)

Dobie Gillis is teenager who wants have girlfriend but he is broke and he wants anything to girlfriend. This was very good show it's so funny and I think it inspired boy meets world Dobie parents and his best friend Maynard are also very good characters

u/Choice-Wind-9283 — 1 month ago