m4nu3lf

m4nu3lf t1_iy53n0j wrote

Given a funtion y(x), then d(y(x))(h) (or dy for short) is the differential of y(x) which is defined as y'(x)*h where y'(x) is the derivative of y(x) with respect to x and h is a new variable.
The same goes for dx where x = i(x) is the identity function with respect to x. So given x' = 1 we have dx = h. So dy(x)/dx is just another way to write y'(x).

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m4nu3lf t1_ivzl2yn wrote

While that's true in most cases, it's not always true. There have been examples of inexperienced people proposing a solution to a problem that actually turned out to be better or correct. Two examples that come to my mind are:

  • One person suggesting to Elon Musk on Twitter to light all the engines of Starship during landing and shutting off two of them. If any engine fails you don't choose it to be the one you rely on for landing.

  • One guy accidentally proving a mathematical hypothesis in a thread about the anime The Melancholy of Harui Suzumiya on 4chan.

Quite funny, although these are, of course, exceptions.

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m4nu3lf t1_iub02h4 wrote

Economic growth is measured in GDP growth. GDP is roughly speaking the monetary value of the goods and services a country producers. The monetary value of a good or service roughly correlates with how much people want that thing. Hence it's almost tautological (trivially true) that people want economic growth.

Indeed economic growth isn't required. It usually just happens as people produce the goods and services they or others want more efficiently or with more resources.

Can growth go on indefinitely? Basically yes. Nowadays a lot of things of value are just information (think about a computer game). We can produce a lot of information. Also, even if there were hard limits to what you could produce, you can have infinite growth by asymptotically getting closer to what is the theoretical maximum without hitting it, although growth will be slower and slower.

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