We examine a polynomial function which has no minimum, but has a finite infimum. This may be surprising, based on intuition for single variable functions. We begin by building up this intuition for single variable functions, before breaking it. To help understand where this example came from, we conclude with further examples of two variable polynomials functions with no minimum.
00:00 Introductory examples
01:44 Non-polynomial examples
04:05 Summary (so far)
05:24 f(x,y) = (1-xy)² + x²
08:02 How did this happen? Example (i)
09:26 Example (ii)
11:01 Example (iii)
12:46 Conclusion
