(no subject)
Random math idea of the day: A "group" is a set of objects (numbers in this case) along with some sort of "operation" (we'll call it +), that has some rules. For clarity's sake let's use the set {0,1,2,3,4} with the understanding that 5 is equal to 0 (i.e. 2+3=0, etc). A group behaves like this:
i) if I take any two numbers in this set and add them together I get that their sum is also in the set. Example: 1+3=4, and 4 is in our set. Similarly, 3+2=0, and 0 is in our set.
ii) For every number in the set, I can add some other number to it and get 0. Here 0 is called the "identity" element of the group because any number plus 0 gives that number back, i.e. x+0=x. So we can add any two numbers and get 0...example: 2+3=0, so 3 is the "inverse" of 2, and 2 is the "inverse" of 3 - they are "inverses".
iii) The associative property is satisfied: (a+b)+c=a+(b+c). This is kind of a technicality, and not really important for all intents.
Some other examples of groups: the real numbers (anything with a decimal, ex: 1, pi, -.000231444,0) with addition, the integers (all positive and negative whole numbers, ex: -3,2,0,1) also with addition, and the real numbers minus 0 using multiplication.
Life isn't bad. I have a final on Monday (Analysis), and I'm looking forward to it. I think that my performance in that class isn't representative of my skill in the subject, so I really need to perform on the final. Often times while pursuing a math degree, the only thing that really matters is how you do on the final. I've had at least two finals that have earned me A's simply because I got 100's on them.
I've been lifting weights consistently and with serious focus, and I'm more fit than I've ever been. I played soccer last sunday, scored three goals, and had one assist, and played some serious defense.
I'm really lucky to have such great friends, and of course to have a beautiful girlfriend who loves me, all of which I'm very thankful for.
I've always thought that I had a lot of talent, mentally speaking at least. However, I wasn't raised with any sort of work ethic, so I probably haven't lived up to my potential so far. That's really the only thing I can complain about, and it's certainly under my control and solvable, so that's cool.
Happy birthday to big P, just to make it a public thing.
Went to the Salt Lick a few days ago, it killed me.
Supplements are kickass when you lift consistently, just fyi.
i) if I take any two numbers in this set and add them together I get that their sum is also in the set. Example: 1+3=4, and 4 is in our set. Similarly, 3+2=0, and 0 is in our set.
ii) For every number in the set, I can add some other number to it and get 0. Here 0 is called the "identity" element of the group because any number plus 0 gives that number back, i.e. x+0=x. So we can add any two numbers and get 0...example: 2+3=0, so 3 is the "inverse" of 2, and 2 is the "inverse" of 3 - they are "inverses".
iii) The associative property is satisfied: (a+b)+c=a+(b+c). This is kind of a technicality, and not really important for all intents.
Some other examples of groups: the real numbers (anything with a decimal, ex: 1, pi, -.000231444,0) with addition, the integers (all positive and negative whole numbers, ex: -3,2,0,1) also with addition, and the real numbers minus 0 using multiplication.
Life isn't bad. I have a final on Monday (Analysis), and I'm looking forward to it. I think that my performance in that class isn't representative of my skill in the subject, so I really need to perform on the final. Often times while pursuing a math degree, the only thing that really matters is how you do on the final. I've had at least two finals that have earned me A's simply because I got 100's on them.
I've been lifting weights consistently and with serious focus, and I'm more fit than I've ever been. I played soccer last sunday, scored three goals, and had one assist, and played some serious defense.
I'm really lucky to have such great friends, and of course to have a beautiful girlfriend who loves me, all of which I'm very thankful for.
I've always thought that I had a lot of talent, mentally speaking at least. However, I wasn't raised with any sort of work ethic, so I probably haven't lived up to my potential so far. That's really the only thing I can complain about, and it's certainly under my control and solvable, so that's cool.
Happy birthday to big P, just to make it a public thing.
Went to the Salt Lick a few days ago, it killed me.
Supplements are kickass when you lift consistently, just fyi.