Search Results for ""

A common mechanism which generates singularities from smooth initial conditions.

A set is said to be bounded from above if it has an upper bound. Consider the real numbers with their usual order. Then for any set M subset= R, the supremum supM exists (in ...

A set is said to be bounded from below if it has a lower bound. Consider the real numbers with their usual order. Then for any set M subset= R, the infimum infM exists (in R) ...

1 calcus=1/(2304).

The relationship Sq^i(x cup y)=Sigma_(j+k=i)Sq^j(x) cup Sq^k(y) encountered in the definition of the steenrod algebra.

If P(x) is an irreducible cubic polynomial all of whose roots are real, then to obtain them by radicals, you must take roots of nonreal numbers at some point.

A sequence a_1, a_2, ... such that the metric d(a_m,a_n) satisfies lim_(min(m,n)->infty)d(a_m,a_n)=0. Cauchy sequences in the rationals do not necessarily converge, but they ...

The definite integral int_a^bx^ndx={(b^(n+1)-a^(n+1))/(n+1) for n!=1; ln(b/a) for n=-1, (1) where a, b, and x are real numbers and lnx is the natural logarithm.

Chained arrow notation is a notation which generalizes the Knuth up-arrow notation and is defined as a^...^b_()_(c)=a->b->c.

A surface with tetrahedral symmetry which looks like an inflatable chair from the 1970s. It is given by the implicit equation The surface illustrated above has k=5, a=0.95, ...