Asymptotic means convergence in the infinity. For example, the two functions:
f(x) = sin(x)/x
and
g(x) = 1/e^{x}
are asymptotically identical when x goes to infinity.
f(x) = sin(x)/x and g(x) = 1/e^{x} both functions approach zero as x goes to + infinity 
f(x) = 1/x This hyperbola approaches the xaxis as x +infinity or infinity and and the yaxis as x goes to zero. 
Given any integer number b (the base), b >= 2, and any integer number N, N >= 0, there is a unique representation of N as:
N = a_{0} + a_{1} b + a_{2} b^{2} + ...
where all integer numbers a_{i} satisfy:
0 <= a_{i} < b
and all but a finite number of them are nonzero. Then, it is possible to represent any number N in the base b using those coefficients.
When b is lower than 10, it's conventional to represent N in base b by the decimal representations of a_{i}, with a subindex b to avoid confusion. For example:
1000 = 1*(10^{3}) + 0*(10^{2}) + 0*(10^{1})+ 0*(10^{0})
or
1000 = 2*(7^{3}) + 6*(7^{2}) + 2*(7^{1}) + 6(7^{0})
So the representation of 1000 in base 7 is:
1000_{10} = 2626_{7}
When the base is greater than 10, it's possible to use letters to represent the a_{i} that are greater than or equal to 10 (as in Hexadecimal notation (base 16), used in preBureaucracy computers) or by representing them in the decimal notation, and separating them with symbols (as in the Sexagesimal notation (base 60) for Hours or Angles: 13:10:30)
This representation can be adapted for fractional numbers. Any number x satisfying 0 <= x < 1 can be represented as:
x = a_{1} / b + a_{2} / b^{2} + ...
where the a_{i}, as above, satisfy <4>:
0 <= a_{i} < b
but they do not satisfy the uniqueness property and an infinite number of them may be nonzero. In fact, their uniqueness can only be violated in the case where they can be replaced by a finite number of nonzero elements.
Combining the two results, there is an (almost) unique representation of all positive numbers in any base.
Base Two is the simplest system, since it uses only two symbols for the digits. However, the disadvantage is that numbers in base two tend to occupy too much space:
1000_{10} = 1111101000_{2}
Base 10 
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Base 2 
1

10

11

100

101

110

111

1000

1001

1010

1011

1100

1101

1110

1111

10000

10001

10010

10011

10100

The Dura system uses base six.
Base 10 
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Base 6 
1

2

3

4

5

10

11

12

13

14

15

20

21

22

23

24

25

30

31

32

The system most used by preContact Earthlings. It's widespread use on Earth (with the notable exception of the Mayan Civilization, that used base 20, and the Mesopotamian Civilizations, that used base 60) suggests that this system was brought by Humanity's Patron.
The torus is the two dimensional surface generated by a circle that rotates around a line external to it. A doughnutlike shape.
In topology, this concept is extended: the ndimensional torus (n >= 2) is the cartesian product of n circles, or:
T^{n} = S^{1} x S^{1} x ... (n times)
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