2007-10-03 01:36:23 · 5 answers · asked by Freebrum 3 in Science & Mathematics ➔ Mathematics
No, not at all. Think about what continuous means. Then think about what a single point is. Actually, a point has no dimensions -- it is a location. It cannot be considered a continous function by any stretch of the imagination.
2007-10-03 01:45:04 · answer #1 · answered by Marley K 7 · 0⤊ 1⤋
by the common statement that a continuous function is a function whose graph can be drawn without lifting the chalk from the blackboard.. A single point on a graph can be a continuous function, provided that point is not a variable.
2007-10-03 01:48:32 · answer #2 · answered by Siva 5 · 0⤊ 0⤋
Yes it can. Specifically, the graph consisting only of the point (a, b) can be considered as the graph of the unique function f:{a} → {b}, which obviously maps a ↦ b. Any such function is vacuously continuous, since the domain consists only of a single isolated point.
2007-10-03 03:17:07 · answer #3 · answered by Pascal 7 · 0⤊ 0⤋
If the area of the functionality is {a million} and the apropriate topology is used, then specific. when you consider which you may in basic terms get "close to" a million with the help of utilising x=a million and the effect is often "close to" 2! i'd evaluate it so. you may get arbitrarily close to y=2 with the help of figuring out on x arbitrarily close to a million. yet what approximately x=a million.01? that's not interior the area ( neither is the different non-"a million" extensive variety!). notice - any determination of ordered pairs IS a functionality, presented that the vertical line try is handed. The set {(a million,2)} constitutes a functionality with area={a million} and variety={2}. not a truly helpful one,yet a functionality however.
2016-10-20 21:36:52 · answer #4 · answered by ? 4 · 0⤊ 0⤋
Not if the function has any variables in it.
2007-10-03 01:39:42 · answer #5 · answered by Anonymous · 0⤊ 1⤋