SLOG week 6

   This week we discussed the concept and definition of a limit. I like limits. The discussion of them has reminded me of what we discussed so long ago in the first week of class, namely, absolute precision.
   Visualizing and "feeling" a limit is quite simple for a given function. If the limit of f is, say, 20 as x approaches 10,  you can easily imagine the line representing the function getting closer and closer and closer and closer to 20 as you start just to the left of 10 and move along the line. It is intuitive, like many concepts in maths.
   The definition of a limit, on the other hand, is not very intuitive at first glance. That is why it makes me think of the absolute certainty of it. It looks unnatural when you look at it the first few times, yet it makes so much sense and it successfully lays out the concept with such precision. If you were to say "well, the function just approaches the limit as x gets closer to the given number", then there are many ways in which people might misunderstand you. Such is the imprecision of the English language; you can explain mathematical concepts, but not without ambiguity. The precision of the mathematical symbols and definitions, however, means that,as long as the symbols and equations are understood, the concept will be captured with complete accuracy. It is not ambiguous.