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Chapter 5
Read the rest of Chapter 2 and send in your responses to these questions
by 7 am Wednesday:
1. Why are the integers not a field?
Integers are only used in conjunction with axioms and are not
themselves as system.
.. therefore cannot be a field.
2. What does the author mean when he says mathematics is becoming
more abstract? Also, give a specific example of increasing abstraction in
a field other than mathematics.
Because Axioms are considered to be true for the numbers they
apply to, the original process is no longer needed.
This makes it possible
to create another set of axioms that apply to the first set, and so on and
so forth.
Each time an axiom is placed, "mathematics" is getting more
abstract.
3. Write a few sentences about the problems with set theory discovered
by Russell.
In set theory, some sets have X property and others don't.
But, Russell
found that because of this property, sets with the property X and sets
without property X, had logically become part of the very sets that they
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 Spring '08
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