ABSTRACT ANALYSIS

ABSTRACT ANALYSIS

1. Abstraction in math

   • the 'skeleton' or core of a problem
     • eg:- algorithms in programs-abstract rules are applied to execute
   • syntax vs semantics
     • completeness theorem
   • numbers- an abstract concept
     • before numbers, comparison was the method to count
     • positive no.s, zero, negative no.s, rational no.s
     • abstract concepts need to be explained
   • math was built using confirmation bias
   • how to count the number of natural,rational,etc?
     • comparing sets; functions
     • cardinal numbers
   • need for abstraction
     • turn circle to line problem
       • impossible due to lack of edges
       • possible by expanding or compressing