Binary Trees?

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Show that a finite binary tree has at least one leaf.

How can I prove this?

2006-11-14 13:32:00 · 2 answers · asked by ifoam 3 in Science & Mathematics ➔ Mathematics

2 answers

My memory on this is hazy, but I think a binary tree can't have any loops, so all its branches have to end.

Also by definition, a leaf has no children. Therefore, the leaves are the end of the structure. How you'd prove this with mathematical symbols I don't know, but the logic seems pretty clear.

2006-11-14 13:42:10 · answer #1 · answered by Anonymous · 0⤊ 0⤋

There must be at least one root entry, or there is nothing there.

2006-11-14 21:38:30 · answer #2 · answered by BurningPyre 4 · 0⤊ 0⤋