Vocab List 1-11
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Commutative | For every x,y belonging to F, there is a x+y=y+x and a x*y=y*x
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| Associative | For every x,y,z belonging to F there is:
(x+y)+z=x+(y+z) and
(x*y)*z=x*(y*z)
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| Closure | For every x,y belonging to F there is x+y belonging to F and x*y belonging to F.
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| Well-Ordering Principle | -Every non-empty sub set of Natural Numbers has a least element.
-If M <= Natural Numbers, then there exists R belonging to M so that R <=a for ever a belonging to M.
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| Induction Principle | (Natural Numbers)
Suppose P(n) is a statement about:
n belonging to Natural Numbers, If we can show
1.P(1) is true.
2.Whenever P(n) is true then P(n+1) is true.
Then P(n) is true for all n.
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| Ordered Field | A field F that is an ordered set with the following additional properties:
1. If x>0 and y>0 then x+y>0
2. If x>0 and y>0 then x*y>0
3. x<y if and only if y-x>0
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| Order | An order on a set S is a relation that satisfies the following:
1. If x,y belongs to S, then exactly one of x<y, x=y, or y<x is true.
2. For all x,y,z belonging to S, if x<y and y<z then x<z.
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| Field | A nonempty set F of objects that has two operations, addition and multiplication, that satisfy the following properties:
-Closure
-Associative
-Identity
-Inverses
-Distributive
-Commutative
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| Distributive | For every x,y,z belonging to F there is x*(y+z)= x*y + x*z
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| Inverses | For every x belonging to F there is -x belonging to F so that x+(-x)=0
For each x belonging to F there is a 1/x belonging to F so that x* (1/x) = 1, x!=0.
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| Identity | For x belonging to F there exists 0 belonging to F so that x+0=x and there exists 1 belonging to F so that x*1=x.
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Review the information in the table. When you are ready to quiz yourself you can hide individual columns or the entire table. Then you can click on the empty cells to reveal the answer. Try to recall what will be displayed before clicking the empty cell.
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If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
rissa230
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