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Properties of the real
numbers
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Properties |
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Examples |
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1 |
a
+ b
= b
+ a, |
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5
+ 3 = 3 + 5, |
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2 |
(a
+ b)
+ c
= a
+ (b
+ c), |
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(2
+ 3) + 5 = 2 + (3 + 5), |
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3 |
a
+ 0
= a, |
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3
+ 0 = 3, |
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4 |
a
+ (-a)
= 0, |
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4
+ (-
4)
= 0,
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5 |
a
· (b
+ c)
= a
· b
+ a
· c, |
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2
· (4 + 7) = 2 · 4 + 2 · 7, |
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6 |
a
· b
= b
· a, |
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6
· 8 = 8
· 6 |
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7 |
a
+ (-b)
= a
-
b, |
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9
+ (-
4)
= 9
-
4 = 5, |
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8 |
-
(a
+ b)
= -
a
-
b, |
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-
(3 + 4) = -3
-
4 = -7, |
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9 |
b
-
a
= -
(a
-
b), |
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5
- 7
= - (7
-
5) = -2, |
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10 |
a
· (-b)
= -
a
· b, |
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3
· (-
5) = -
3
· 5 =
-15, |
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11 |
(-a)
· (-b)
= a
· b, |
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(-
3)
· (-
6) = 3
· 6 = 18, |
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12 |
-
(-a)
= a, |
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-
(-
7) = 7 |
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13 |
a
· 0
= 0, |
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(-
11)
· 0 = 0,
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14 |
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15 |
a
· 1
= 1
· a
= a, |
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-
5
· 1 = 1
· (-
5) = -
5, |
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16 |
(-1)
· a
= -
a, |
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(-1)
· 4 = -
4, |
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17 |
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18 |
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19 |
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20 |
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21 |
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22 |
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23 |
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24 |
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25 |
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26 |
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27 |
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28 |
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if |
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since |
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29 |
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if |
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since |
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Functions
contents A |
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Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
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