Proving that a function is grounded

Question

I need to prove that a function $f:[0,1]\times[0,1]\rightarrow [0,1]$, which is nondecreasing in each variable, is grounded (i.e. that $f(0,y)=0=f(x,0)$ for all $(x,y)$ in $[0,1]\times[0,1]$). Additionally, it is known that $f(t,1)=t=f(1,t)$ for all $t$ in $[0,1]$.

Answer 1

Because $f(t, 1) = t = f(1 , t)$ for all $t$ in $[0, 1]$, that means that $f(0, 1) = 0 = f(1, 0)$. This also implies that $f$ is grounded, which follows straightforward from the def'ns.