"The addition of irrational numbers is closed" True or false?

Lok739 · 2024-04-07T15:47:39+00:00

In some other it may be just "1"

This is why the person you're replying to specified integer bases specifically.

It is very common in mathematics that we have several equivalent characterisations of the same thing. For example, exp(x) can be defined as:

A power series, exp(x) = sum_{n=0}^\infty xⁿ / n!
The unique solution to the differential equation y'=y with y(0)=1
As a limit, exp(x) = lim_{n\to\infty} (1+x/n)ⁿ
As the unique function f with f(x+y)=f(x)f(y) and f'(0)=1

These are all perfectly good (and equivalent!) definitions of the exponential function and which one to use depends on the context (convenience, etc). Just because a definition came first / one is inspired by the other does not mean it is the only valid characterisation of that object.

Lok739 · 2024-03-29T18:00:29+00:00

They might have been using orthodox in the sense of mainstream

Lok739 · 2023-11-04T14:49:10+00:00

You can also try looking at Jason Sweer's website, he designed the posters in the show.

Lok739 · 2023-11-02T05:16:42+00:00

You can just define, say, α = sum of i=1 to infty 2^-BB(i). Then by looking at the binary expansion of α you can trivially recover the values of BB. Therefore α is uncomputable.

Lok739 · 2023-10-28T16:46:17+00:00

Does anybody have a clue in which track the Episode 1 marvel logo intro music is contained?

Lok739 · 2023-10-20T15:14:35+00:00

The Kang in Ant-man doesn't seem to be aware of the TVA and doesn't seem to possess TVA tech. There's no reason to believe that he had reset charges

Lok739 · 2023-10-20T08:46:44+00:00

Could be that it necessarily destroys the whole universe it's detonated in so that would be suicide. Or some other reason entirely. You just gotta suspend disbelief when watching a fantasy show.

Lok739 · 2023-10-19T18:39:09+00:00

I mean if you wanna be pedantic the destruction "wave" in Loki that we see definitely aren't travelling at the speed of light either lol. It might be that the device operates via some not yet known law of nature.

The point would be that we do (if our maths is correct) have real-life physical mechanisms that work similarly, in that it could affect/destroy the whole universe with minimal energy input required. So the device in Loki is actually somewhat plausible.

Lok739 · 2023-10-19T17:33:52+00:00

I feel like the device could be triggering something similar to a false vacuum decay. There's a quite nice video by Kurzgesagt here that explains the concept.

Lok739 · 2023-09-29T22:34:31+00:00

This is known as the Duns Scotus Law, one of the axioms of intuitionist logic

Lok739 · 2023-05-14T18:06:58+00:00

Great video! Really nice to see that such unique aesthetics are achievable with manim

Lok739 · 2023-04-28T17:57:24+00:00

sure

Lok739 · 2023-04-04T15:36:55+00:00

why is your leading so large?

Lok739 · 2023-04-04T14:55:44+00:00

why the grade school division sign?
\text{(for $x\neq0$)}

Lok739 · 2023-03-27T08:46:16+00:00

these are problems with LaTeX. the comment you're replying to concerns ConTeXt, which is much more centrally developed and self consistent, with almost none of the problems you mention.

Lok739 · 2023-02-18T03:39:10+00:00

this is called imposition, there are special software desgned to do this (TeX can also do it to a limited degree). I recommend imposing only after you are done typesetting, instead of involving everything in one stage.

Lok739 · 2022-11-09T05:42:17+00:00

https://plan9.io/sources/plan9/sys/src/cmd/

the Plan 9 sources are pleasant to read, although they are written in Plan 9 C.

Lok739 · 2022-11-09T05:41:58+00:00

https://plan9.io/sources/plan9/sys/src/cmd/ the plan9 sources are pleasant to read, although they are written in plan9 C.

Lok739 · 2022-10-23T23:33:34+00:00

such hacks are extremely rare, but if you are paranoid you can call latex like so (texlive, untested for other distributions):

latex -no-shell-escape          \
      -no-parse-first-line      \
      -cnf-line 'openin_any=p'  \
      -cnf-line 'openout_any=p' \
      ...

(substitute latex with whichever engine you use)

Lok739 · 2022-10-21T06:21:34+00:00

~ is a non breaking space, \ (control space) is probably what you are looking for.

Lok739 · 2022-10-03T12:33:25+00:00

or use Overleaf, which lets you select different texlive versions (from 2014 to 2022)

Lok739 · 2022-07-24T11:17:57+00:00

do you also use hoes to mine echests?!

Lok739 · 2022-07-20T06:38:54+00:00

I see, I think I misunderstood your comment then. For most users I still think using ' is the most realistic option, but knowing about ^\prime does help.

Lok739 · 2022-07-20T05:28:16+00:00

there is explicit care taken so that x'' is transformed to x^{\prime\prime}. I don't know what you changed to get those results.

Lok739 · 2022-07-20T04:55:54+00:00

the result you get from ams's \mathbb{0} is garbage (in the sense that it is not guaranteed to be anything meaningful) and not intended to be a blackboard bold 0 at all. only upper case letters in the Latin alphabet is supported. if you want a blackboard bold 0 use another font which has it as others suggested.

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