That’s hard to say, really. I don’t know enough about the history of math to know whose work was really groundbreaking at the time, though I would say Euler , Gauss , Ramanujan , Erdős , and Shelah were/are all geniuses
Why do you ask?
Sure thing.
Erm, I suppose. Like, I use functions at work, in programming. I make a function called DoSomething and allow it parameters (a, b, c) and when I put in values for a, b and c I end up with new stuff that has to do with what the values of a, b and c are.
MyAnswer = DoSomething(1,2,3)
Function DoSomething(a,b,c)
iAnswer = a + b + c
DoSomething = iAnswer
End Function
Response.write MyAnswer
So the above would write out “6” because I put 1, 2 and 3 as a, b and c and my function added them.
Same thing?
Seems like algebra so far to me…heh
Have you seen Finite Simple Group, and if so, what did you think?
I ask because I’m curious to know what sorts of colleges and/or universities put out such fine, knowledgable and generous people, such as yourself.
Oh, I didn’t know that it happened so fast. That’s interesting. I suppose it is hard to think of “foundational” math systems which were widely believed for a long time, and only later proven inconsistent. So, yeah, like you said, it’s easy to believe in the consistency of the large cardinal hypotheses on the grounds that no inconsistency has been found in so long. It’s easy, but it still makes me uneasy… 
Ah. I imagine you just had a brain fart, but, in case not, if alpha is weakly inaccessible in V, then, I believe, alpha is strongly inaccessible in L, since GCH holds in the constructible universe, and thus you obtain Con(ZFC).
I’m terrible at math but I am really impressed by it. I would like to be better at it. A lot better at it. How do I get better at math?
By the way, thanks for the great bio links!
Funny. Better than I thought it would be, as I don’t usually like corny math jokes or undergraduate a capellla groups
See, what I remember is that if \kappa is strongly inaccessible, then V_{\kappa} is a model of ZFC, and I don’t know as much about L as I should, so…
All are Wikipedia
Do math problems.
How much math education have you had? Are you in school?
You didn’t say this before. Of course you know what functions are!
L**esson 2: Limits involving functions from R to R (i.e., domain and range are both the real numbers)
**
For this course, we will only deal with functions whose domain and range are the real numbers.
How do we normally picture functions? Well like this:
Normally we draw them on the cartesian plane, where the horizontal axis represents the domain, and the vertical axis the range.
Some common functions
Now remember that for every guy in the domain, a function must spit out only one guy in the range. Or to put it another way, the vertical line test
But you know this already, right?
Well, let me define a silly function as follows.
f(x)=2 if x is not 7, and f(7)=100
What does it look like? It is a flat line (at height 2) with an infinitely small ‘hole’ in it (at the spot x=7), and above that ‘hole’ (at the height of 100) there is a single point floating there. Got the picture? Like this
except our line is horizontal.
This function is a good tool for us to describe limits. A limit of a function at a point is the value that function as that function gets really close to, but not equal to, that point. So the limit of f(x) as x approaches 7 in our example above is 2, because even though at 7 f(x)=100, everywhere near 7 except 7 itself, f(x)=2.
Now a warning: a limit does not have to exist.
1)f(x)=1 if x<4
and f(x)=2 if x>4 or x=4
Then the limit as x approaches 4 of f(x) does not exist. Why? Well, assume it did. Then look at f(x) as x gets really close to 4 on the left side. Surely it must be 1! But then look at f(x) as x gets really close to 4 on the right side. Surely the limit must be 2! Well a number can’t be both 1 and 2. Therefore, no limit.
- Read this page
Does the class have any questions?
What is set theory?
In “I don’t know a thing about math” terms, please
I’m afraid I never got training in formal logic, it’s the part of our Philosophy class that the professor skipped. I don’t know if it was because it looked scientific (he hates the physical sciences, don’t ask me why) or because we already were perfectly able to split hairs lengthwise, diagonally or sideways without any need for official training.
… for the post before mine, wouldn’t the function in 1) have a “limit on the right” and a “limit on the left”? That’s not the same as “no limit”, is it?
Have you studied geometry beyond trig and a few areas?
Ooh, I’ve got another one. We’re doing some stuff involving Jacobians (for double and triple integrals) in class this week, and there are some things the textbook doesn’t bother to explain (and the professor hasn’t discussed it in class). For instance, how did Jacobi come up with the Jacobian, and why does the Jacobian work?
I don’t generally think that I can explain math in non math terms. (I realise you said “I don’t know a thing about math” terms, which is a bit different, but this is something that comes up at parties). Notice what ZipperJJ asked and how I answered, and how 4.66 answered. I don’t mean to pick on 4.66, actually most other mathematicians would answer like that. But I want to take a stand! I think people deserve the long explanation! If it is too much for some, that is their loss; at least I tried. I think you lose too much accuracy in an analogy. Sometimes, at parties when people ask me to explain what I study, I say something like “it would take too long to explain.” I try to explain that I don’t think they are stupid, but just that there is too much prerequisite knowledge, but I’m sure they still think I’m a jerk. Hence only sometimes.
It is possible often to give analogies, especially when time is at issue (I don’t usually have a few hours to explain at a party). I could tell you, for example, that I study Borel Equivalence Relations (which is considered a part of Set Theory these days), and that this involves showing that some math problems are harder than other math problems, but I don’t think you would actually have learnt anything.
That said: Right here I was starting to type out an intro to set theory, but this article does a much better job than I can, plus they have cool pictures and fonts.
This is a very good point. In mathematics, as in Philosophy, it is important to agree on your definitions beforehand. What you have said is perfectly reasonable, and true I suppose, but let it be known that when we say the limit exists (without qualifying on the left/right) it is implicitly meant that the two ‘sided’ limits exist and are equal.
No reason you should’ve gotten that from my previous post, as I didn’t mention it. My bad.
Yes, I took a course which used this text. We discussed Euclidean geometry (including proving that there are only 5 Platonic solids ), spherical geometry, and projective geometry. It is quite a good book, I think. But even this is ‘classical’ geometry, I think. That is, I don’t think I know any Algebraic Geometry beyond the basics, and I sure as heck don’t know any Differential Geometry.
I don’t generally think that I can explain math in non math terms. (I realise you said “I don’t know a thing about math” terms, which is a bit different, but this is something that comes up at parties). Notice what ZipperJJ asked and how I answered, and how 4.66 answered. I don’t mean to pick on 4.66, actually most other mathematicians would answer like that. But I want to take a stand! I think people deserve the long explanation! If it is too much for some, that is their loss; at least I tried. I think you lose too much accuracy in an analogy. Sometimes, at parties when people ask me to explain what I study, I say something like “it would take too long to explain.” I try to explain that I don’t think they are stupid, but just that there is too much prerequisite knowledge, but I’m sure they still think I’m a jerk. Hence only sometimes.
It is possible often to give analogies, especially when time is at issue (I don’t usually have a few hours to explain at a party). I could tell you, for example, that I study Borel Equivalence Relations (which is considered a part of Set Theory these days), and that this involves showing that some math problems are harder than other math problems, but I would feel like I’m pulling a fast one.
That said: Right here I was starting to type out an intro to set theory, but this article does a much better job than I can, plus they have cool pictures and fonts.
This is a very good point. In mathematics, as in Philosophy, it is important to agree on your definitions beforehand. What you have said is perfectly reasonable, and true I suppose, but let it be known that when we say the limit exists (without qualifying on the left/right) it is implicitly meant that the two ‘sided’ limits exist and are equal.
No reason you should’ve gotten that from my previous post, as I didn’t mention it. My bad.
Yes, I took a course which used this text. We discussed Euclidean geometry (including proving that there are only 5 Platonic solids ), spherical geometry, and projective geometry. It is quite a good book, I think. But even this is ‘classical’ geometry, I think. That is, I don’t think I know any Algebraic Geometry beyond the basics, and I sure as heck don’t know any Differential Geometry.
Guess who left their wife logged in? And then simulposted under her name?
It’s just all the partial derivatives in matrix form, no? Seems natural enough, but then I am biased. What do you mean, “why does it work?” What does it do that you are curious about?
Maybe I’m just being dense. Why would the the determinant of the partial derivatives in matrix form give you a constant to multiply by when you’re changing the variables for integration? I mean, it certainly doesn’t sound intuitive to me, but maybe I’m missing something.
Sorry, I misunderstood your question. What you are referring to, I believe, is the mutivariable version of integration by substitution (see especially the bottom of the page.) Of course you remember from calc II that integration by substitution works because of the chain rule .