Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper velocity
Division by zero cookie in half. The problem with 5 cookies and 0 people cannot be solved in any way that preserves the meaning of "divides". Another way of looking at division by zero is that division can always be checked using multiplication. Considering the example above, setting "x" = , if "x" equals ten divided by zero, then "x" times zero equals ten, but there is no "x" that, when multiplied by zero, gives ten (or any number other than zero). If instead of "x" = we have "x" = , then every "x" satisfies the question 'what number "x", multiplied by