Here is more or less what my physics professor said at one point in class today. I didn't hear perfectly but I think it captures the main idea.
"Let's assume that 'epsilon' is infinitely large..." (calculations)... "Now let's assume 'epsilon' is zero..." (calculations)... "Are you guys following me?" (clearly we weren't, as indicated by the quietness of our response) "That's a very small 'yes'... Now let's assume that the 'yes' is large......."
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