
About the irrationality of e=2.718... (1840) - dondinis
http://fermatslibrary.com/s/about-the-irrationality-of-e
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siegelzero
This a very terse proof. It is stated "The same method can also be used to
prove that e cannot be a root of a second degree equation with rational
coeﬃcients", but if I recall correctly, the generalization for the
irrationality of $e^2$ isn't entirely straightforward, mainly due to the
presence of powers of 2 in the terms of the expansion.

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arglebarnacle
Off topic, but can you tell me whether you're using a browser extension to
render $e^2$ (and if so which one!), or if you're simply using the $ character
as a delimiter for humans who read and write a lot of LaTeX code?

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simplicio
I always found it weird that despite being developed at CERN and most widely
used in the early years by universities and research labs, HTML never
developed a decent standard for transmitting/rendering math equations (I know
that there's a math tag now, but it doesn't seem to get much use). Especially
given that Latex would seem to provide a pretty widely known de-facto standard
for the syntax.

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nikdaheratik
1) HTML is derived directly from SGML which was used to handle similar markup
issues in printed texts. One of the reasons why HTML was successful was
because there were already similar tools in place from SGML that could be
quickly applied to handle processing and correctness. Adding math would
require building a number of additional tools.

2) TeX by itself doesn't resolve very well into the DOM tree which is what
parsers use to organize the markup data internally. You need a markup language
that is similar to HTML if you want to make it easy for browsers, parsers, and
libraries to adopt the new standard.

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conistonwater
It's curious how "when b is <0" was considered okay scientific French, but in
English these days it looks terrible and is written as "when b<0".

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klodolph
The way math papers and proofs are written is fascinating, because it reveals
so much about how people read mathematical notation. Much of the older
notation was more explicitly used as shorthand for words or phrases, rather
than being a language in its own right (as it is today). (And old papers were
written out in natural language, which seems so hard to read by today's
standards.)

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taserian
I especially like how certain symbols we regularly use nowadays weren't always
known that way. For example, the set of integers is now written as \mathbb{Z}
, but used to be written as a fraktur "Z" with a bar above.

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fred256
I love how matter-of-factly the article ends with "so, etc."

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sizzzzlerz
Funny how my geometry teacher back in high school didn't offer that up as a
means of completing any of the proofs we had to do. It would have made
finishing my homework so much faster.

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ydah
The article is about e^1 tho

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tjalex
Check out the annotations on the side of the document for more details -- you
can extend the proof to e^2 easily with c = 0.

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khana
e. Irrational -and- Transcendental.

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waynecochran
For the transcendental part, wouldn't you have to prove that e is not the root
of _any_ polynomial with rational coefficients (not just a quadratic)?

