Search found 12 matches

Sun Jan 24, 2010 6:20 am UTC
Forum: Mathematics
Topic: Algebra: Negative Exponents
Replies: 10
Views: 1927

Re: Algebra: Negative Exponents

Actually I was thinking of exponentiation as a set of unary operators a^{x} , one for each x. This is more of an abstract algebra viewpoint, since in Group theory, a^{x} only makes sense when x is an integer, yet a could be any group element, which is probably not an integer or even a number of any ...
Sat Jan 23, 2010 10:14 pm UTC
Forum: Mathematics
Topic: Algebra: Negative Exponents
Replies: 10
Views: 1927

Re: Algebra: Negative Exponents

Well, any way you look at it, the negative exponent (or any exponent) is undoubtedly an operator. Your book may not consider it one because it is not a binary operator. Your standard operators +, -, x, /, all require two "input" numbers. A exponentiation operation is unary, so it requires ...
Fri Jan 22, 2010 4:17 pm UTC
Forum: Mathematics
Topic: Cardinality of the gaussian integers
Replies: 16
Views: 2392

Re: Cardinality of the gaussian integers

One way to order them is a + bi < c + di if a < b or (a=b and c < d). It is easy to see this is a strict well-ordering and isomorphic to \left \langle \omega,< \right \rangle . Okay, first of all you mean a<c or a=c and b<d, not what you wrote. But this is still false, since you have essentially de...
Fri Jan 22, 2010 12:48 am UTC
Forum: Mathematics
Topic: Cardinality of the gaussian integers
Replies: 16
Views: 2392

Re: Cardinality of the gaussian integers

Nope, their cardinality is aleph-null, exactly the same as the integers. You can think of a single gaussian integer as an ordered pair of integers, and all sets of n-tuples of integers for n < \omega have cardinality aleph null. One way to order them is a + bi < c + di if a < b or (a=b and c < d). I...
Sat Jan 16, 2010 6:10 am UTC
Forum: Mathematics
Topic: Mathematics and intellect
Replies: 85
Views: 9508

Re: Mathematics and intellect

I only knew 3 of them. I have never even heard of a xylem or bauxite or filtrum. I think more appropriate questions would be like "How does an airplane wing work?" or "How do you know if a star is going to turn into a black hole?". Questions that are not overly specific, yet requ...
Fri Jan 15, 2010 5:05 pm UTC
Forum: Mathematics
Topic: roomies
Replies: 8
Views: 1208

Re: roomies

I spent some free time at work and found a partial solution. On my first attempt I was able to solve it in 7 swaps (so 8 nights total), so I am fairly confident that with a little more work, it can be reduced to 6 or maybe even 5 swaps. Here is my algorithm for how I did it. For notation, order the ...
Thu Jan 14, 2010 4:10 pm UTC
Forum: Mathematics
Topic: Mathematics and intellect
Replies: 85
Views: 9508

Re: Mathematics and intellect

Whether mathematicians are actually more intelligent than other intellects probably has no definite answer, as the definition of "intelligence" is too ambiguous. Who are we to say that a mathematician is smarter than a great poet or engineer? Certainly we excel at one particular type of th...
Mon Jan 11, 2010 7:52 pm UTC
Forum: Mathematics
Topic: Which math should I take next year?
Replies: 15
Views: 2076

Re: Which math should I take next year?

I would also recommend linear algebra. It certainly has just as many proofs and abstract concepts as other theories. I think it is also a very important prerequisite for moving onto any other abstract algebra, as various types of vector spaces are frequently used as examples of different algebraic s...
Thu Jan 07, 2010 7:21 pm UTC
Forum: Logic Puzzles
Topic: 2 puppies
Replies: 132
Views: 18540

Re: 2 puppies

The people who are getting 1/2 are thinking of "the probability of the puppy we don't know being male" versus "The probability of the whole system". If we assume puppy A is male, then puppy B has a 1/2 chance of being male. But since in the entire system of two puppies there are ...
Wed Jan 06, 2010 11:10 pm UTC
Forum: Logic Puzzles
Topic: 2 puppies
Replies: 132
Views: 18540

Re: 2 puppies

Unfortunately the way the question is worded leaves too much ambiguity. Normally the way this question is worded, that's the case, but I think this OP did an admirable job of making it unambiguous. whoops, yeah I was thinking along the lines of "what's the probability of the other puppy being ...
Wed Jan 06, 2010 10:21 pm UTC
Forum: Logic Puzzles
Topic: 2 puppies
Replies: 132
Views: 18540

Re: 2 puppies

Unfortunately the way the question is worded leaves too much ambiguity. The probably could either be 1/3 or 1/2, and this probability solely depends on how you obtain the information. If you were to go to the pet store, not being able to look at either puppy, and choose one at random, your probabil...
Wed Jan 06, 2010 9:34 pm UTC
Forum: General
Topic: Who the dickens are you?
Replies: 10922
Views: 2380059