carloswilson

I am aware. It is typically represented as Z_5. They are called prime fields.

I highly doubt wsxcde meant prime fields in their comment though. wsxcde seemed to be talking about the set of all integers and the set of all real numbers in their comment. Only the latter is a field (and a ring) whereas the former is only a ring.

And (-a)(-b) = ab holds in rings (and thus fields).

> The set over which the field is defined (Z or R)

What? The set of all integers, Z, is not a field! R is. But Z isn't. Z is a ring, a commutative ring. I doubt you understand what a field is!

> already contains -3, -2 etc.

Yes, and those elements are literally the additive inverses of their positive counterparts. If you disagree with this, then the numbers -3, -2, etc. literally have no meaning.

> It then turns out that -3 is the additive inverse of 3.

Are you making this all up with your original research or do you have any proper literature written by a professional mathematician to back it up?

> Also, this post conflates the unary negation operator with negative numbers.

-a is a standard way to represent additive inverse of an element in field.

The point about "unary negation operator" seems irrelevant.

In the real number field, additive inverse of a positive real number is indeed the negative of that number. The negative of that number is also obtained by the application of unary negation operator on the positive number.

The additive inverse of 3.14 is -3.14. Unary negation operator applied to 3.14 gives us -3.14. I don't see how conflating unary negation operator with negative numbers here is any issue here.

I appreciate that answering questions in a grilling interview is more difficult than asking questions, but ...

> “You don’t know? This was the largest data scandal with respect to your company, that had catastrophic impacts on the 2016 election. You don’t know?”

... but at the same time, I would certainly expect the chairman and CEO of a company to be more prepared to answer these difficult questions than what is reported in the original article. This was one of the biggest scams related to Facebook. I understand that Zukerberg's legal team may have advised him to be vague during the interview and he probably answered what is best for his company.

But as citizens of the world, we should never find such vague answers acceptable. The way Cambridge Analytica has upset the process of democracy and how Facebook data was used while doing so requires Facebook to be subject to such grilling. It should be made clear to Facebook in no uncertain terms that it needs to present answers and concrete answers.

> So I don’t know what the solution is to these types of accidental UI bugs.

Obviously a scroll bar should be an acceptable solution? Why do designers hate scroll bars these days?

Prior to GMail, we used to check our "Junk" folder occasionally in whatever email service we used.

When GMail arrived with its nice spam classification, it was great. Worked well, better than any competitors out there. This gradually conditioned us to ignore the "Spam" directory completely. Now things have moved to the opposite extreme. It is quite difficult to host independent email servers and send emails from it without GMail classifying it as spam. The high false-positive rate has become the norm. Instead of GMail trying to reduce the false-positive rate, it has now become the responsibility of those hosting email servers to jump through the hoops to ensure that their emails are not classified as spam.

Makes one think: If we knew what we know today about spam and abuse of Internet services, would SMTP have been designed the way it is designed today? What fundamental design change could have made it immune to spam? Perhaps a pull-based design instead of push-based? Perhaps something even cleverer?