Giant brains; or, Machines that thinkBerkeley, Edmund Callis
Science
Giant brains; or, Machines that think
Berkeley, Edmund Callis
Computers -- Popular works
A _power_ of any number _a_ is _a_ multiplied by itself some number
of times. _a_ × _a_ × _a_ ... × _a_ where _a_ appears _b_ times is
written _a_ᵇ and is read _a_ to the _b_th power. _a_², a to the 2nd
power, is _a_ × _a_ and is called _a squared_ or the _square_ of _a_.
_a_³, _a_ to the 3rd power, _a_ × _a_ × _a_, is called _a cubed_, or
the _cube_ of _a_. _a_⁰, _a_ to the zero power, is equal to 1 for every
_a_. _a_¹, _a_ to the power 1, is _a_ itself. The first power is often
called _linear_. _a_ to some negative power is the same as 1 divided
by that power; that is, _a_⁻ᵇ = 1/_a_ᵇ. _a_⁻¹, _a_ to the power minus
1, is 1/_a_, and is called the _reciprocal_ of _a_. _a_¹ᐟ², _a_ to
the one-half power, is a number _c_ such that _c_ × _c_ = _a_, and is
called the _square root_ of _a_ and often denoted by √_a_.
table, tabular value, argument, etc.
An example of a _table_ is:
0.025 0.03
+——————————————————
1 | 1.02500 1.03000
|
2 | 1.05063 1.06090
|
3 | 1.07689 1.09273
The numbers in the body of the table, called _tabular values_, depend
on or are determined by the numbers along the edge of the table, called
_arguments_. In this example, if 1, 2, 3 are choices of a number _n_,
and if 0.025, 0.03 are choices of a number _i_, then each tabular value
_y_ is equal to 1 plus _i_ raised to the _n_th power. _n_ and _i_ are
also called _independent variables_, and _y_ is called the _dependent
variable_. The table expresses a _function_ or _formula_ or _rule_. The
rule could be stated as: add _i_ to 1; raise the result to the _n_th
power.
constant
A number is said to be a _constant_ if it has the same value under
all conditions. For example, in the formula: (area of a circle) = π ×
(radius)², π is a constant, equal to 3.14159 ..., applying equally well
to all circles.
infinity
Mathematics recognizes several kinds of infinity. One of them occurs
when numbers become very large. For example, the quotient of 12 divided
by a number _x_, as _x_ becomes closer and closer to 0, becomes
indefinitely large, and the limit is called _infinity_ and is denoted ∞.
equation, simultaneous, linear
An example of two linear simultaneous _equations_ is:
7_x_ + 8_t_ = 22
3_x_ + 5_t_ = 11
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