Showing All Field Axioms for a Tuple of Real Numbers

In this exercise we will cover all 9 field axioms for a tuple of real numbers with a special addition and multiplication.

⏰ Timeline 00:00 Exercise 00:15 Commutativity of addition 00:45 Commutativity of multiplication 01:08 Associativity of addition 01:48 Associativity of multiplication 03:10 Additive identity 03:38 Multiplicative identity 04:27 Additive inverse 05:05 Multiplicative inverse 05:56 Distributivity 07:05 Conclusion

🔢 Ring definition R x R := {(a,b) | a,b in real numbers } (a,b) + (c,d) := (a+c, b+d) (a,b) * (c,d) := (ac - bd, ad + bc)

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