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format: markdown
categories: math
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# Algebra
*Note: Most of the definitions and notation in the section are based on [^rudin] or [^meserve].*
----------- ----------------- -------------- --------------- ---------- --------------------- --------
Name Symbol Pos. Integers? Pos. Rationals? Rationals? Reals (wrt Pos Int.)? Complex?
----------- ----------------- -------------- --------------- ---------- --------------------- --------
addition $a + b$ Y Y Y Y Y
product $a\times b$ Y Y Y Y Y
subtraction $a-b$ N N Y Y Y
division $\frac{a}{b}$ N Y Y Y Y
power $a^b$ Y Y Y Y Y
root $\sqrt{\text{a}}$ N N N Y Y
----------- ----------------- -------------- --------------- ---------- --------------------- --------
Table: Closure of binary operators on given sets of numbers
## Definitions
involution
: to raise a number to a given power
evolution
: to take a given root of a number
associative
: $(a+b)+c=a+(b+c)$
commutative
: $a+b=b+c$
distributive
: $(a+b)c=ac+bc$
[^rudin]: **Principles of Mathematical Analysis (3rd ed)**, by Walter Rudin. McGraw-Hill, 1976
[^meserve]: **Fundamental Concepts of Algebra**, by Bruce Meserve.
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