124 karma · joined July 26, 2023
Musk is and will forever be woefully underprepared to fight against someone with Mark’s training and level of fitness. His challenge to fight was childish and idiotic. Even smart people do idiotic things from time to time.
This isn’t a claim that everyone agrees this is literally a basic human right. It’s a colloquialism to emphasize the author’s view that this is something that should have been granted to the workers long ago and that it is appalling that it wasn’t.
Please don’t get hung up on semantics. Use a different phrasing if it pleases you to do so.
It is good to have well maintained roads. It is not good to have what the U.S. has.
As many as 1,000 officers and army soldiers raided the Imperial Palace on the evening of 14 August 1945 to destroy the recording. The rebels were confused by the layout of the palace and were unable to find the recordings, which had been hidden in a pile of documents. The two phonographs were labelled original and copy and successfully smuggled out of the palace, the original in a lacquer box and the copy in a lunch bag. Major Kenji Hatanaka attempted to halt the broadcast at the NHK station but was ordered to desist by the Eastern District Army.[2][3]
Even after two were dropped members of the armed forces still wanted the war to continue.
The grand bargain you speak of has already occurred. It occurs when Congress passes a budget that is signed by the President.
Every Uber driver I’ve had in US and Canada are happy with driving for Uber. One guy I had the other day drives under as his second job and He says it pays his rent, his car payment and gas and his primary job goes straight to savings.
I wrote a comment using similar logic. Every child I've met working in mines was happy to be able to provide money for their family.
The logic is bad. It's poor reasoning to say, "Every person I've met doing X is happy. Therefore letting people do X is a good thing." I was pointing that out.
They don’t think of Log(z) as a set of values. At least I don’t. I assume one means the principal branch when writing Log(z) unless specifically stated otherwise. Maybe in their mind they do think of an infinite set when seeing Log(z). I’m skeptical of this possibility though.
Of course the function that gives you inverse images is nothing more than an inverse function that is allowed to give multiple values.
You can’t use the word function for something that isn’t a function. It makes no sense to say inverse function that is allowed to give multiple values. Hence the need for terms like pre-image of a set.
In all contexts it is important that a function yield a single value for a given input because that is the definition of the word.
EDIT: Complex analysis was developed well before the formal definition of functions, relations, set theory. As such there are legacy terms in use. Mathematics has a lot of abuse of notation. For instance x=2 can mean assignment or an equation to solve. It depends on context.
In each branch of a multi-function the mapping is a function and, as a convenience, a single term “multi-function” is used to encapsulate all this. It cuts out the verbosity. A multi-function is not a function though.
My pedantry in this comes from the blog post. It was poorly written and left out some, from a mathematical point of view, important details. For instance the author uses a Schauder basis and has an uncountable sum at one point whilst ignoring the need distinguish between a Hamel basis and Schauder basis or the need to use a linear ordering in the reals to properly make sense of the uncountable sum.
Function spaces can’t always be viewed as vector spaces because there may be no concept of addition of functions or a concept of scalar multiplication on the functions that behaves well with whatever notion of addition the functions satisfy.