Boundary between discrete&continous

[cheungyl]

what is the real boundary(or difference) between discrete&continous(as the title)? my major is physics and i find that scientists are dealing with the different treatment to these two kinds of phenomenons, but what is the real boundary? by this i mean what they actually are and how they ARE DIFFERENT from each other? we know that there is something like a transition,but will transitions really be found? I consider this a math problem so i write it here. is any mathematician working with this? (forgive my poor english)

 

[farleyknight]

I am not an expert on this subject, but probably the best way to describe how they are different (in terms of elementary math) is to consider a number like pi or Euler's e or the square root of 2. These numbers cannot be expressed in terms of a finite set of other numbers. You need an infinite sum of numbers to express it in exact terms. Without an infinite set of terms, you can only produce an approximation.

There are definitely others, but finite vs infinite is perhaps the easiest analogy.

Surely some one can chime in about Cantor's uncountability proof.

 

[cheungyl]

i know what u mean. Discrete in physics is born from infinity inf maths. thank u !

 

[awkward]

Personally, I would say that continuous mathematics has to do with limiting processes. Continuity, limits of sequences, differentiation, integrals-- these all have to do with limiting processes, one way or another.