MIDYEARS

So like don't be expecting too much XD I did say I had midyears.

Kind of happy about my trial exams marks. I did about ten or so chem exams before the Chem Trial, and then watched Glee the night before, and pulled an ok score. Not to the standard of the year 12 group last year; they would rip me for getting so much wrong! But it was all cool. I know what to study more now xD

PSYCH was not too hard. Just alot of detail missing. Sad...was beaten. probably only going for Psych Prize this year ^^ Maths and Sciences are just for the freaks XD

I was really interested in this proof, but it turned out to just be a definitional thing. what a let down:

PROOF 1+1=2:

The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:

P1.  1 is in N.
P2.  If x is in N, then its "successor" x' is in N.
P3.  There is no x such that x' = 1.
P4.  If x isn't 1, then there is a y in N such that y' = x.
P5.  If S is a subset of N, 1 is in S, and the implication
    (x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1, then define a + b = a'
    (using P1 and P2). If b isn't 1, then let c' = b, with c in N
    (using P4), and define a + b = (a + c)'.

Then you have to define 2:
Def:  2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem:  1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.
    Then 1 + 1 = 1' = 2  Q.E.D.

Note: There is an alternate formulation of the Peano Postulates which
replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the
definition of addition to this:
Def: Let a and b be in N. If b = 0, then define a + b = a.
    If b isn't 0, then let c' = b, with c in N, and define
    a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:

Proof: Use the second part of the definition of + first:
    1 + 1 = (1 + 0)'
    Now use the first part of the definition of + on the sum in
    parentheses:  1 + 1 = (1)' = 1' = 2  Q.E.D.

http://mathforum.org/library/drmath/view/51551.html

Yeah I'm kind of sad like that.

Got a bit of new music from a good friend. Going through it all now...really is opening up my mind to new types of music other than the stuff I used to listen to xD HELPING MY MUSIC EDUCATION. YAYYY ain't it good? ^^

GLEEEEEE I quite love the singing...and I only recently found this!



GOOD LUCK PEEPS~