mathgrad

3 ms·

1. 1.▲
   by mathgrad 13y ago

   I am a mathematician I don't need examples. What is your formal definition of a mapping. In mathematic it is normally used as a synonym for a morphism in a given category and in the category of sets this would be a function. So in our
2. 2.▲
   by mathgrad 13y ago

   Look up Peano arithmetic to see how one proves 1+1 = 2 within the standard formal system.
3. 3.▲
   by mathgrad 13y ago

   A function is a relation for elements in a to elements in b such that for every element in a there is a unique element in b. This is vacuously true of the empty relation when a is empty.
4. 4.▲
   by mathgrad 13y ago

   There is a very natural definition of numbers as sets. We define 0 to be the empty set and we define the successor function by S(x) = {x} union x. Then the natural numbers are the smallest set containing 0 and closed under the successor ope
5. 5.▲
   by mathgrad 13y ago

   This is not true. A very natural way to define a^b is as the number of functions for a set with "b" elements to a set with "a" elements. In this case there is exactly one function from the empty set to the empty set, and