File:Continuous Functions – Non-continuous 2d-example (view 3).svg
Summary
| Description |
English: The function f: R²→R, f(x,y)=f(0,0):=0 for x=y=0 and f(x,y):=xy/(x²+y²) otherwise, is not continuous in (0,0), despite f_y: R→R, f_y(x):=f(x,y) for any fixed y is continuous just as is f_x: R→R, f_x(y):=f(x,y) for any fixed x. Deutsch: Die Funktion f: R²→R, f(x,y)=f(0,0):=0 für x=y=0 und f(x,y):=xy/(x²+y²) andernfalls, ist nicht stetig im Punkt (0,0), obwohl für beliebiges festes y f_y: R→R, f_y(x):=f(x,y) stetig ist wie auch für beliebiges festes x f_x: R→R, f_x(y):=f(x,y). |
| Date | |
| Source | Own work |
| Author | Xantares |
| SVG development | Category:Valid SVG created with Mathematica:Diagrams#Continuous%20Functions%20–%20Non-continuous%202d-example%20(view%203).svg  Category:Translation possible - SVGThis diagram uses embedded text that can be easily translated using a text editor. |
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