Information Technology Reference
In-Depth Information
That function is
⎧
⎨
0
,ifx
≤
N
/
3
3
x
N
μ
h
(
x
)=
−
/
≤
≤
/
1
,ifN
3
x
2
N
3
⎩
1
,if
2
N
/
3
≤
x
≤
N
and then
⎧
⎨
1
,if
0
≤
x
≤
N
/
3
μ
h
(
3
x
N
,ifN
x
)=
1
−
μ
h
(
x
)=
−
/
≤
≤
/
2
3
x
2
N
3
⎩
/
≤
x
and with them it can be recognized that an opposite, or antonym, of h is
0
,if
2
N
3
⎧
⎨
⎫
⎬
⎭
=
μ
h
(
1
,if
0
≤
x
≤
N
/
3
3
x
N
μ
ah
=
μ
h
(
N
−
x
)=
2
−
,ifN
/
3
≤
x
≤
2
N
/
3
x
)
.
⎩
0
,if
2
N
/
3
≤
x
Thus, under the representation of the antonym by the symmetry
x
,the
antonym of heap coincides with the negation of heap given by the negation func-
tion
N
α
(
x
)=
N
−
x
, something that seems to be in agreement with the inexistence
of antonyms of the term heap in the dictionaries of antonyms. Familiarity with the
term heap requires, at least, familiarity with not-heap, once it is understood as an
antonym (not regular, of course). On the contrary, how could a heap be recognized
as such?
(
x
)=
1
−
15.4.2
Undoubtedly, a heap is constitued by grains although it is not perceived through
the number of grains it contents, but by its three-dimensional shape captured by
a balance between the area of its basement, and its height. For instance, with a
small basement and a large height, the heap will go down. A representation of this
characteristic of heaps can be reached through its volume, that if, for instance, the
heap is
•
Apyramid,is
V
=
1
/
3 (area of the base
×
height)
r
2
•
A circular cone, is
V
=
1
/
3
(
π
×
×
h
)
, with
r
the radius of the circle's base,
and
h
the height.
In the same vein that to recognize that John is tall can be reached by comparing
John's height with the height of someone that we know is tall (a prototype), and
with another person that we know either that is not tall, or that is short (an anty-
prototype), to recognize that a set of grain is a heap can be obtained by comparison
with something we know can be called a heap, and something that cannot be called
a heap. To fix the universe, let us only consider heaps in the unit cube
3
.
[
,
]
0
1
