oooo oooo
o o o o
o o o o ooooo ooooooo ooooooo <- Give the smiley
o o o o awesome new sunglasses
o o o o for your chance to win
oooooo oooooo a free Xbox 360!
o o
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Name:
Anonymous2009-10-15 18:34
This thread sucks. I will use it to post some poetry.
I read some SICP the other day
That was a really nice book
I can't keep reading, my boss is a crook
Gives me too much work and too little pay
/prog/ will be spammed continuously until further notice. we apologize for any inconvenience this may cause.
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Anonymous2013-08-31 7:43
Cardinality is studied for its own sake as part of set theory. It is also a tool used in branches of mathematics including combinatorics, abstract algebra, and mathematical analysis. In category theory, the cardinal numbers form a skeleton of the category of sets.
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Anonymous2013-08-31 8:27
All the remaining propositions in this section assume the axiom of choice:
If κ and μ are both finite and greater than 1, and ν is infinite, then κν = μν.
If κ is infinite and μ is finite and non-zero, then κμ = κ.
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Anonymous2013-08-31 9:13
The practice of refusing infinite values for measurable quantities does not come from a priori or ideological motivations, but rather from more methodological and pragmatic motivations.
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Anonymous2013-08-31 9:58
Elementary set theory can be studied informally and intuitively, and so can be taught in primary schools using Venn diagrams. The intuitive approach tacitly assumes that a set may be formed from the class of all objects satisfying any particular defining condition.
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Anonymous2013-08-31 10:44
The surreal numbers are a proper class of objects that have the properties of a field.
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Anonymous2013-08-31 11:29
Hence S breaks up into uncountably many orbits under G. Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset X of S with the property that all of its translates by G are disjoint from X. The set of those translates partitions the circle into a countable collection of disjoint sets, which are all pairwise congruent.