## Thursday, October 21, 2010

### So I tried 'Star Wars, the force unleashed II, Demo' on PS3 for half an hour.

Of course I was not being nice, did not play along and built all sorts of contraptions. But hey ... I was simply using 'the force' the way Vader taught me.

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## Sunday, October 17, 2010

### Know your induction, deduction and logical implication.

Induction:

Induction in colloquial English means 'educated guess', Mathematical induction however, is a kind of deductive reasoning, unlike plain 'induction'.

Deduction:

An argument is valid if it is impossible both for its premises to be true and its conclusion to be false. An argument can be valid even though the premises are false.

Deductive arguments are generally evaluated in terms of their validity and soundness, For a deductive argument to be considered sound the argument must not only be valid, but the premises must be true as well.

Logical implication:

Many writers draw a technical distinction between the form ``p implies q " and the form ``if p then q ". In this view, writing ``p implies q " asserts the existence of a certain relation between the logical value of p and the logical value of q while writing ``if p then q " simply forms a compound sentence whose logical value is a function of the logical values of p and q . Notice that a relation is a mathematical object while a sentence, whether open or closed, is a syntactic form that exists in the domain of signs.

How young students understand this: Students' understandings of logical implication

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## Friday, October 15, 2010

### sqrt(prime) is irrational proof as an excuse for latex training Proving that the square root of a prime number is a basic discrete math exercise, here is my proof (using my first latex document ever).
Final pdf:
Source tex file:

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## Thursday, October 7, 2010

### Integer remainder repetition

I was just trying to solve a discrete math problem, when I bumped into the following:
take 2 prime numbers A and B, when you starting taking multiples of A, the remainders of those multiples after division by B will change at every multiple, and within B repetitions, they would have produced all possible remainders, this is quite 'intuitive' if we take an example.
Let us take 11 and 7.
11 x 1 = 7 x 1 + 4
11 x 2 = 7 x 3 + 1
11 x 3 = 7 x 4 + 5
11 x 4 = 7 x 6 + 2
11 x 5 = 7 x 7 + 6
11 x 6 = 7 x 7 + 3
11 x 7 = 7 x 11 + 0

The sequence of remainder is quite interesting: 4,1,5,2,6,3,0.
I guess it is possible to derive an equation for it depending on the 2 numbers but for now let us try to prove that within 7 multiples of 11, all possible remainders are generated.

It is not very hard: 