When comparing between two spanning trees to see which one is "better", argue that the Minimum Spanning Tree (MST) defined as the tree that has the minimum sum of weights of its edges, is the same tree that is smaller than all other trees if we just determine which is smaller among 2 trees by comparison rather than addition.

Comparison rather than addition refers:

Suppose we square the weights of the edges in G. In other words, we have the same graph G

except every edge e has a squared weight w1(e) = w(e)^2. The shortest path tree now might

change compared to what you have before. If we change the tree by squaring the weights

again, until two successive shortest path trees are identical. Thus, these shortest paths now can be defined with no

reference to the actual weights. i.e., given two paths instead of evaluating whether path p1

is shorter than path p2 can be determined just by comparing weights, without having the

operation of addition of weights.