User neil - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T12:20:15Z http://mathoverflow.net/feeds/user/5555 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/22247/geometrical-meaning-of-grassmann-algebra Geometrical meaning of Grassmann Algebra Neil 2010-04-22T20:01:02Z 2012-09-04T07:52:20Z <p>I don't understand wedge product and Grassmann algebra. However, I heard that these concepts are obvious when you understand the geometrical intuition behind them. Can you give this geometrical meaning or name a book where it is explained?</p> http://mathoverflow.net/questions/23478/examples-of-common-false-beliefs-in-mathematics/23626#23626 Answer by Neil for Examples of common false beliefs in mathematics. Neil 2010-05-05T20:45:47Z 2010-05-05T20:52:06Z <p>$n!$ is the product of all positive integers less than or equal to $n$. In fact it should be defined in combinatorial terms.</p> <p>Many assume the fact that parallel lines in Euclidean geometry do not cross is an axiom, while it can easily be proved in terms of vector space.</p> <p>Many lecturers do not stress the difference between inner product and scalar product and most students think that these are different names for the same thing.</p> <p>In complex numbers $i = \sqrt{-1}$. Obviously it is not correct as well.</p> http://mathoverflow.net/questions/23478/examples-of-common-false-beliefs-in-mathematics/23626#23626 Comment by Neil Neil 2010-05-06T01:19:59Z 2010-05-06T01:19:59Z @sigfpe What the definition above has to do with product of sets? http://mathoverflow.net/questions/23478/examples-of-common-false-beliefs-in-mathematics/23626#23626 Comment by Neil Neil 2010-05-05T22:24:18Z 2010-05-05T22:24:18Z I believe a definition through product to be poor since it considers $0!$ as a special case. Of course one can axiomatize Euclidean geometry as he want, however in my opinion to call the fact about the parallel lines an axiom is the same as to call Pythagorean theorem an axiom (you can build the set of axioms including it). http://mathoverflow.net/questions/22247/geometrical-meaning-of-grassmann-algebra/22657#22657 Comment by Neil Neil 2010-05-04T22:27:23Z 2010-05-04T22:27:23Z The book is just awesome.