I have this math logic class and have wired question... Would really appreciate if any one can help with this question... Thanks
The language of number theory is L is {0,S,+,.,E,<}
where 0 is the constant symbol for number zero, S is the successor function S(x)=x+1, the symbol . means multiply. The symbols +, < means what you expect. E stands for exponentiation, so E(3,2)=9
Assume that L-formulas will be interpreted with respect to the nonnegative integers and write an l forluma to express the claim that p is a prime number. Can you write the statement of Lagrange's Theorem (which states that every natural number is the sum of four squares)? What is the formal statement of the Twin Primes Conjecture (which says that there're infinitely many paires (x,y) such that x and y are both prime and y=x+2?
The language of number theory is L is {0,S,+,.,E,<}
where 0 is the constant symbol for number zero, S is the successor function S(x)=x+1, the symbol . means multiply. The symbols +, < means what you expect. E stands for exponentiation, so E(3,2)=9
Assume that L-formulas will be interpreted with respect to the nonnegative integers and write an l forluma to express the claim that p is a prime number. Can you write the statement of Lagrange's Theorem (which states that every natural number is the sum of four squares)? What is the formal statement of the Twin Primes Conjecture (which says that there're infinitely many paires (x,y) such that x and y are both prime and y=x+2?