myslsl

I'm sorry my mom called you "pretty fucking dumb". I know that must have hurt your feelings.

This feels pretty fucking dumb.

So you're saying that because a religion allows you to choose which of God's commandments, carefully passed down through every generation, you personally want to follow based on your gut feeling, can't be shamed?

No, that is not what I said.

Why should the ones who choose to deny parts of their religion be seen as representative of it over those who've chosen to uphold them?

I definitely answered this in my original comment.

Because if the majority of people following a particular religion reject a prior view as false or wrong, then arguably that view is no longer part of the religion.

Religions aren't crisp, unchanging, monolithic entities where everybody believes the same thing forever. If we're talking about judaism in the sense of the views and practices jewish people actually subscribe to, then that seems like we are referring to beliefs they actually hold in a mainstream/current sense, not beliefs they previous held but now reject?

This seems a little hyperbolic of you.

Ain't nothin' but a heartache.

The punchline here is a little compact. I don't feel like it really gives the closure I need. Maybe if the basis for the joke had more continuity the humor would be less discrete.

Operating System Concepts by Silberschatz, Galvin and Gagne is a classic OS textbook. Andrew Tanenbaum has some OS books too. I really liked his OS Design and Implementation book but I'm pretty sure that one is super outdated by now. I have not read his newer one but it is called Modern Operating Systems iirc.

i has nice real world analogues in the form of rotations by pi/2 about the origin (though this depends a little bit on what you mean by "real world analogue").

Since i=exp(ipi/2), if you take any complex number z and write it in polar form z=rexp(it), then multiplication by i yields a rotation of z by pi/2 about the origin because zi=rexp(it)exp(ipi/2)=rexp(i(t+pi/2)) by using rules of exponents for complex numbers.

More generally since any pair of complex numbers z, w can be written in polar form z=rexp(it), w=uexp(iv) we have wz=(ru)exp(i(t+v)). This shows multiplication of a complex number z by any other complex number w can be thought of in terms of rotating z by the angle that w makes with the x axis (i.e. the angle v) and then scaling the resulting number by the magnitude of w (i.e. the number u)

Alternatively you can get similar conclusions by Demoivre's theorem if you do not like complex exponentials.

They don't eventually become 1. Their limit is 1 but none of the terms themselves are 1.

A sequence, its terms and its limit (if it has one) are all different things. The notation 0.999... represents a limit of a particular sequence, not the sequence itself nor the individual terms of the sequence.

For example the sequence 1, 1/2, 1/3, 1/4, ... has terms that get closer and closer to 0, but no term of this sequence is 0 itself.

Look at this graph. If you graph the sequence I just mentioned above and connect each dot you will get the graph shown in this picture (ignoring the portion to the left of x=1).

As you go further and further out along this graph in the positive x direction, the curve that is shown gets closer and closer to the x-axis (where y=0). In a sense the curve is approaching the value y=0. For this curve we could certainly use wordings like "the value the curve approaches" and it would be pretty clear to me and you that we don't mean the values of the curve itself. This is the kind of intuition that we are trying to formalize when we talk about limits (though this example is with a curve rather than a sequence).

Our sequence 0.9, 0.99, 0.999, ... is increasing towards 1 in a similar manner. The notation 0.999... represents the (limit) value this sequence is increasing towards rather than the individual terms of the sequence essentially.

I have been trying to dodge the actual formal definition of the limit of a sequence this whole time since it's sort of technical. If you want you can check it out here though (note that implicitly in this link the sequence terms and limit values should all be real numbers).

I will fucking piledrive you if you mention AI again.