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That which does not kill us makes us soggy and hard to light.

THE MOST COMMON ERRORS IN UNDERGRADUATE MATHEMATICS

In particular I need to look at:

"Some more advanced students (e.g., college seniors) use the implication symbol ($\implies$) as a symbol for the phrase "the next step is." A string of statements of the form


 * $A \implies B \implies C \implies D$

should mean that A by itself implies B, and B by itself implies C, and C by itself implies D; that is the coventional interpretation given by mathematicians. But some students use such a string to mean merely that if we start from A, then the next step in our reasoning is B (using not only A but other information as well) and then the next step is C (perhaps using both A and B), etc.

Actually, there is a symbol for "the next step is." It looks like this: $\leadsto$ It is also called "leads to," and in the LaTeX formatting language it is given by the code \leadsto. However, I haven't seen it used very often."
 * Such a distinction seems unnecessary, especially considering theorems such as Extended Rule of Implication. Surely at each step of the way we have an implied $\land$ going on everything before it? --GFauxPas 04:23, 12 February 2012 (EST)