"Consider a function(aka curve)..." Thank you for this answer and I apologize for the ambiguity in my question, especially, regarding the word "curve." By "cu

"Consider a function(aka curve)..." Thank you for this answer and I apologize for the ambiguity in my question, especially, regarding the word "curve." By "curve" I meant "curved line" or even more precisely, a "curved line without a gap." Obviously this is an assumption; I ignore if the line is made of points; because I want to compare a curved line with a straight line. So I believe that the question is not about "continuity." (By the way Galileo has a nice discussion about lines and points here http://books.google.com/books?id=SPhnaiERbWcC&dq=galileo%20galilei&pg=PA26#v=onepage&q&f=false http://books.google.com/books?id=SPhnaiERbWcC&dq=galileo...) Maybe I can ask the same question like this. Here are 3 numbers: 0.0872664626; 0.1047197551; 0.1221730476. Is it possible to tell if these are points on a straight line or if they are points on a curved line? I believe both; depending on the scale they are plotted; the numbers would look like a straight line on some scale; but they are points on a sin curve. In other words, nature does not distinguish between straight line and curved line; the same three numbers can be read both ways. So I am looking for a theorem that would describe this fundamental property of nature. Thanks.