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Math feels like discipline with no reward.

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marshall
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17 Feb 2012, 6:22 pm

Declension wrote:
marshall wrote:
As for math being absolutely true in every universe I'm not so sure. Not all mathematical logicians have made up their mind on whether the axiom of choice is "true".


I don't think that the axiom of choice is the sort of thing that is either true or false. However, the statement "in ZF, the axiom of choice is equivalent to the well-ordering principle" is true in every possible world. Metamathematics is absolutely true.

The axiom of choice is equivalent to the well-ordering principle if ZF and the rules of first-order logical induction are true. I suppose what I just said is nonsense anyways as it's impossible to even talk about the "truth" of logical induction without making reference to logical principles in the language. My brain already hurts.



Declension
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17 Feb 2012, 6:26 pm

marshall wrote:
The axiom of choice is equivalent to the well-ordering principle if ZF and the rules of first-order logical induction are true.


No, that's not what I'm saying. I am not saying that the axiom of choice is true or false. I am not saying that the well-ordering principle is true or false. I am not saying that the axioms of ZF are true or false. I am not saying that the laws of first-order induction are valid or invalid.

What I am saying is that the statement "In ZF, the axiom of choice is equivalent to the well-ordering principle" is true. Translated, this means that I am saying that there exists a proof with the following properties:
(1.) Every line is either an axiom of ZF or is deduced from the previous lines in accordance with the rules of first-order induction.
(2.) The last line says "the axiom of choice is equivalent to the well-ordering principle".

This really is true. If you don't believe it, then you can write the proof, which is a way to show that the proof exists.



blahblah123
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17 Feb 2012, 7:34 pm

NakaCristo wrote:
In mathematics you hardly need to memorize anything! It consist in understanding truth. New problems in mathematics usually require completely new techniques to solve them. Only computers follow rules and steps blindly, mathematicians understand these rules and derive new ones, which then can be used by computers.

There are lots of mathematical problems which have remain unsolved for many years. They are not going to be solved only following rules. They will be solved (if solved sometime) by using a great creativity.


Coming up with new techniques in math is actually very easy. One day when I was using my TI-89 calculator the phrase "SYNTAX ERROR" popped up on the screen. I came up with something completely original - something even the calculator couldn't solve.



heavenlyabyss
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20 Feb 2012, 6:23 am

Yep, you are right. Personally, I love math, and so that is why I do well with it.

I hate writing and poetry and so I do not do well in those areas.

In school, you have to just trudge through the subjects you have no interest in. If you have no interest in math, it is going to be difficult for you. Do your best, but always put your primary focus on what sparks your interest the most.



NakaCristo
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20 Feb 2012, 8:05 am

blahblah123 wrote:
NakaCristo wrote:
In mathematics you hardly need to memorize anything! It consist in understanding truth. New problems in mathematics usually require completely new techniques to solve them. Only computers follow rules and steps blindly, mathematicians understand these rules and derive new ones, which then can be used by computers.

There are lots of mathematical problems which have remain unsolved for many years. They are not going to be solved only following rules. They will be solved (if solved sometime) by using a great creativity.


Coming up with new techniques in math is actually very easy. One day when I was using my TI-89 calculator the phrase "SYNTAX ERROR" popped up on the screen. I came up with something completely original - something even the calculator couldn't solve.


But a syntax error only means that the text was meaningless, if you write random characters you would get it with high probability. And randomness is not originality.

And creating a problem that no one can solve is not very difficult. It is solving a problem that a resisted many intents which is difficult.



blahblah123
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20 Feb 2012, 1:41 pm

NakaCristo wrote:
But a syntax error only means that the text was meaningless, if you write random characters you would get it with high probability. And randomness is not originality.

And creating a problem that no one can solve is not very difficult. It is solving a problem that a resisted many intents which is difficult.


I know. I just felt like trolling that day.



The_Sleeper
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20 Feb 2012, 2:05 pm

Maths is it's own reward, it's fun.