- #1
Shackleford
- 1,656
- 2
I recently bought Real Analysis by Haaser and Sullivan. Is this a good introductory real analysis book? I really bought it for fun. I'm not going to put a formal real or complex analysis course in my math minor.
Well, I'm on page two at the ordered pair proof.
Why is an ordered pair defined as {{a}, {a, b}} ?
(a, b) = (c, d) if a = c and b = d.
Either {a} = {c} and {a, b} = {c, d}
or
{a} = {c, d} and {c} = {a, b}
I understand the second one. If the two sets are equal, then all of the elements in both sets are the same. So, I guess it's irrespective of the number of elements in each set as long as they're all the same.
For the first one, a = c, and b = c or d. Obviously, if b = d the proof is satisfied. However, why does b equal c or d?
Well, I'm on page two at the ordered pair proof.
Why is an ordered pair defined as {{a}, {a, b}} ?
(a, b) = (c, d) if a = c and b = d.
Either {a} = {c} and {a, b} = {c, d}
or
{a} = {c, d} and {c} = {a, b}
I understand the second one. If the two sets are equal, then all of the elements in both sets are the same. So, I guess it's irrespective of the number of elements in each set as long as they're all the same.
For the first one, a = c, and b = c or d. Obviously, if b = d the proof is satisfied. However, why does b equal c or d?