Wrong! It is perhaps the mathematician's lament that pencils are so often pressed upon him dogmatically. Pens, they say, cannot be erased and are thus are literally Hitler.
We shall now document the woeful account of the standard grind 'em up beauties.
Lack of consistency. Either you get super thin precise lines or super fat lines, and the sweet spot in the middle is just too difficult to maintain.
SNAP! Uh oh, it broke, and now you have to use up quite a bit more to resharpen it (and get up to go to the sharpener again). And after it gets sharpened too many times it's trash. Or you can try to hold onto a pencil half the size of your finger (hand cramps incoming!).
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Well, surely our mechanical friends correct these problems and grant us great erasure, yes? No! They suffer from similar problems.
A quarter of each piece of lead is useless, and must be thrown away. Which also means if one of your pieces of lead is snapped in half, its total life got cut by half, ouch.
Click once lead is too short, click twice lead is too long.
Oh, and that your lead can snap off and form a point, and then you're really screwed.
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But despite all of these problems it's worth it, right, because you can erase. Yes and no. You can erase, but we all know from experience that this isn't a perfect process. Erase something once, and you can get away with it, but stuck on a hard problem in math and this is what you're left with: http://25.media.tumblr.com/tumblr_ltbo8blvM41qmyny3o1_500.jpg.
Congrats.
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So we return to our evil pal the pen. I used to tout pencils, but I switched soon thereafter, because pens are grossly superior. It has consistent writing, doesn't require reloading often, and won't smear after a minute has passed. The only negative is that you can't erase, which is just fine if you're not being dumb. Screw up on a page long problem? Get out a new page (you'd have to anyway if you were using pencil anyway). Screw up a line? Single line strikeout or diagonal strikeouts are clean, easy to read, and work out just fine.
So please, put down your pencils, and pick up ink. For the children.
None.