Don't mind me...just setting up some threads for more of my stupidity this upcoming semester.
UNSW course outline: https://www.maths.unsw.edu.au/sites/...81-s2_2016.pdf
Can I please have my proof checked?
The video solution was clever in how it used a Pythagorean identity here to match up A and B, however I did it by solving. Just want to check on its validity
A is a proper subset of B, since there are elements in B that are not in A. You are claiming that A is the set B itself.
Recall that sinx = 0 does not imply cosx = 1
The solutions to sinx = 0 can be divided into the solutions to cosx = 1 and cosx = -1
Edit: sorry did not read the final line
Yes it looks good.
Last edited by Paradoxica; 26 Jul 2016 at 10:37 AM.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
They don't have an answer so I am suspecting that my answer is wrong lol. I started from the outside in my working.
Edit: After line 2 one of my friends used associativity like this
But ends up with a final answer of just instead. Is this justified?
Last edited by leehuan; 27 Jul 2016 at 3:37 PM.
Last edited by leehuan; 27 Jul 2016 at 3:38 PM.
To get the final answer your friend got (which looks correct), use an absorption law at the second last line of your proof. (Unfortunately your simplification in your last line isn't valid. But if we just apply the absorption law there we'll get the answer. )
(See: https://proofwiki.org/wiki/Absorptio...h_Intersection.)
Last edited by InteGrand; 27 Jul 2016 at 3:43 PM.
Yes what your friend did is valid. Since intersection is both associative and commutative, we can do intersections in any order (like, (X cap Y) cap Z = X cap (Y cap Z) = X cap (Z cap Y) = (X cap Z) cap Y, using associativity and commutativity. I used 'cap' to mean intersection symbol.). Then using absorption law finishes it.
Don't view "," and "|" in the same way (btw ":" is a common alternative for "|" that is my personal preference). The former is basically informal formatting here, whilst the latter is part of the formal set builder notation syntax.
{x in A: Mathematical statement P(x) about x}
is the general way of denoting the collection of x in A such that P(x) is true. Comma is just formatting of that mathematical statement in this case, to be translated as "for some". Although this certainly isn't unambiguous notation, its intended meaning should be pretty obvious from context. We are often slightly lazy in writing mathematical statements because writing things formally with quantifiers in each line would be needlessly tedious in long proofs.
Currently studying:
PhD (Pure Mathematics) at ANU
B Arts / B Science (Advanced Mathematics), UNSW
This bugger.
I can see why it is but how would you prove it
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