Howlers Out of the Mouths of Actual Math Students--Part III

A cyclical quadrilateral is an animal that has been taught to ride a bicycle.

Question: A man has x miles to travel. He goes a miles by train, b miles by boat, and c miles on foot. How far has he left to travel?
Student: d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w miles.

Question: Decide whether or not the groups H and K are isomorphic.
Student: H is isomorphic but K is not.

Question: Show that the function f:Z→Z gven by f(x)=2x-1 is one-to-one.
Student: f(1)=1, so f is one-to-one.

A circle is the locust of all points equidistant from a given point.

Let f(x) be a manic polynomial.

0 is an element of the empty set since the empty set contains nothing.

In response to question if a certain series was convergent, one student applied the ratio test and concluded that it was convergent. As a check, he applied another test and discovered that the series was divergent. So, his final answer: "This series is conditionally convergent."

An example of the failure of the law d(x,y) = d(y,x) is that it is longer from New Year's Day to Christmas Day than it is from Christmas Day to New Year's Day.