When I was in college, one CS professor explained the difficulty of coding to me in terms of discreteness vs continuity. In the real world, things are continuous. If you accidentally build your structure with 9 supports instead of 10, then you only lose 10% of the strength of the structure, more or less. The strength varies continuously with the amount of support. But if you're writing a 10-line program and you forget one of the lines (or even one character), the program isn't 10% wrong, it's 100% wrong. (For example, instead of compiling and running correctly, it doesn't compile at all. Completely different results.)
Of course this logic doesn't hold up all the time. Sometimes you can remove a critical support and collapse a structure, and sometimes removing a line of code has little to no effect, but the point is that in programming, a small change can have an unboundedly large effect, which is the definition of discontinuity.
Of course this logic doesn't hold up all the time. Sometimes you can remove a critical support and collapse a structure, and sometimes removing a line of code has little to no effect, but the point is that in programming, a small change can have an unboundedly large effect, which is the definition of discontinuity.
(I believe it was this professor, who was my teacher for discrete math: http://www.cs.virginia.edu/~jck/ )