Fixed-point property of a closed interval
= Fixed-point property of a closed interval
For continuous $f:[0,1]\to[0,1]$, the function $f(x)-x$ is nonnegative at zero and nonpositive at one, so the <intermediate value theorem> gives a fixed point.
= Fixed-point property of a closed interval
For continuous $f:[0,1]\to[0,1]$, the function $f(x)-x$ is nonnegative at zero and nonpositive at one, so the <intermediate value theorem> gives a fixed point.