/sci/ - Science & Math

http://en.wikipedia.org/wiki/Relevance_logic

Another idea I have is to pull m out and use

<span class="math">\sqrt{1 + x} = \sum_{n=0}^\infty \left(\frac{(-1)^n(2n)!}{(1-2n)(n!)^2(4^n)}\right)\ x^n = 1 + \textstyle \frac{1}{2}x - \frac{1}{8}x^2 + \frac{1}{16} x^3 - \frac{5}{128} x^4 + ...[/spoiler]

<span class="math">x:=2(\frac{n}{m})^2[/spoiler]

<span class="math">r \ge m \ge 0[/spoiler]

might be that for larger n, this series is surjective on some relevant codomain

>>4611558
I'm not sure how of if that connects the dots. Both these things handle (computational) operations, which could represent stating the formulas of physics, which in principle give answers from certain inputs.
For this parts it's interesting, but what I want to get at here is the object as intuitive concept. E.g. a child has an understanding of time, and this doesn't even seem to be formal in a level that you can syntactically write it down. I want to handle the intuitive physical concepts.

Please give me some comments on topos theory and what it is good for.

Saltwater fish are evolved to deal with water constantly rushing out of their bodies. The salt in the surrounding water exerts what is called osmotic pressure on the fish. Thus saltwater fish have evolved to be constantly drinking water and excreting salts. When you put a saltwater fish into freshwater, it continues to drink heavily and excreet salt. Thus the fish quickly loses too much salt, and its body begins to react accordingly; nervous impulses are unable to travel, and the fish's CNS shuts down, causing it to die.

There are however many saltwater fish that are able to travel into freshwater, as they have adaptations to change their behavour and biology radically. Pacific salmon are a perfect example of this, and they are called anadromous fish. Also many species have evolved to live in brackish waters, an intermediate between salt and fresh, and can usually tolerate larger differences salinity.