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Some Related Sentences
If and number
If in any one calculation Ptolemy had had to invoke 83 epicycles all at once
, while Copernicus never required more than one third this
number, then
( in
the sense obvious to Margenau
) Ptolemaic astronomy would
be simpler than Copernican
.
If your state has no provisions for
the numbering
of pleasure boats
, you must apply for a
number from
the U.S. Coast Guard for any kind
of boat with mechanical propulsion rated at more than 10 horsepower before it can
be used on Federal waterways
.
If a nation wished to get a head start in physical fitness over all
other nations
, it would start its kindergarten students on a program
of gymnastics
the day they entered and thus eliminate a large
number of the problems
that plague American schools
.
If no specific organization plan exists limiting
the number of scientists at
each salary level
, the result
is a department top-heavy with high-level
, high-salaried personnel ''
.
If we thus spent our very first day in
the midst
of a large
number of your people honoring a new hero and a great national achievement
, our last day
, to us at least
, was equally impressive and very moving
, even though
the crowds were absent and there was almost complete silence
.
If a wedge-shaped coating
of increasing thickness
is removed from a substrate
by an instrument like
the Hesiometer with a knife
of constant rake angle
, a
number of removal mechanisms are often observed which depend upon
the thickness
of the coating
.
If all
the operating variables were varied simultaneously
, Af operations would
be required to do
the same job
, and as R increases this increases very much more rapidly than
the number of operations required
by the dynamic program
.
If Rock shows up during
the number -- or you hear anything -- give me
the signal ''
.
If one takes
the middle
number, 5
, and multiplies it
by 3
( the base
number of the magic square
of three
), the result
is 15
, which
is also
the constant sum
of all
the rows
, columns
, and
two main diagonals
.
If so
, it might
be worth while to assign a future jazz show to a different department -- one with enough confidence in
the musical material to cut down on
the number of performers and give them a little room to display their talents
.

*
If it
is required to use a single
number X as an estimate for
the value
of numbers
, then
the arithmetic mean does this best
, in
the sense
of minimizing
the sum
of squares
( x < sub > i </ sub > − X )< sup > 2 </ sup >
of the residuals
.
If its minimal polynomial has degree
, then
the algebraic
number is said to
be of degree
.
If K
is a
number field
, its ring
of integers
is the subring
of algebraic integers in K
, and
is frequently denoted as O < sub > K </ sub >.

* Let Q
be a set enclosed between
two step regions S and T
. A step region
is formed from a
finite union
of adjacent rectangles resting on a common base
, i
. e
. S ⊆ Q ⊆ T
. If there
is a unique
number c such
that a
( S
) ≤ c ≤ a
( T
) for all such step regions S and T
, then a
( Q
)
If a description
of s
, d
( s ),
is of minimal length
( i
. e
. it uses
the fewest
number of characters ), it
is called a minimal description
of s
. Thus
, the length
of d
( s
) ( i
. e
. the number of characters in
the description
) is the Kolmogorov complexity
of s
, written K
( s ).
If a
) testimonies conflict one another
, b
) there are a small
number of witnesses
, c
) the speaker has no integrity
, d
) the speaker
is overly hesitant or bold
, or e
) the speaker
is known to have motives for lying
, then
the epistemologist has reason to
be skeptical
of the speaker's claims
.
If we take in our hand any volume ;
of divinity or school metaphysics
, for instance ; let us ask
, Does it contain any abstract reasoning concerning quantity or
number?
If a
is algebraic over K
, then K
, the set
of all polynomials in a with coefficients in K
, is not only a ring but a field: an algebraic extension
of K which has
finite degree over K
. In
the special case where K = Q
is the field
of rational numbers
, Q
is an example
of an algebraic
number field
.
If the two carbon atoms at
the double bond are linked to a different
number of hydrogen atoms
, the halogen
is found preferentially at
the carbon with fewer hydrogen substituents
( Markovnikov's rule ).
If F
is an antiderivative
of f
, and
the function f
is defined on some interval
, then every
other antiderivative G
of f differs from F
by a constant: there exists a
number C such
that G
( x
) = F
( x
) + C for all x
.
If there
is no
number to its left
, simply look at
the column headed " 1 " in
the previous row
.
If the game has been scored correctly
, the total
number of plate appearances for a team should equal
the total
of that team's runs
, men left on base
, and men put out
.
If the other player also knows to offer sacrifices
, the expert also has to manipulate
the number of available sacrifices through earlier play
.
If and times
If Af denotes
the space
of N
times continuously differentiable functions
, then
the space V
of solutions
of this differential equation
is a subspace
of Af
.
If amber
is heated under
the right conditions
, oil
of amber
is produced
, and in past
times this was combined carefully with nitric acid to create " artificial musk " – a resin with a peculiar musky odor
.
If this particular quasar and our galaxy could
be seen side
by side at
the same distance
, the quasar would
be 5 magnitudes
( or 100
times ) brighter than our galaxy
.
If a detector was placed at a distance
of 1 m
, the ion flight
times would
be X and Y ns
.

Pasternak later said
, "
If, in a bad dream
, we had seen all
of the horrors in store for us after
the war
, we should have been sorry not to see Stalin go down together with Hitler: an end to
the war in favour
of our allies
, civilized countries with democratic traditions
, would have meant a hundred
times less suffering for our people than
that which Stalin again inflicted on it after his victory
.
If a 4
, 5
, 6
, 8
, 9
, or 10
is thrown on
the come-out roll
( i
. e., if a point
is set ), most casinos allow pass line bettors to take odds
by placing from one to five
times ( and at some casinos
, up to 100
times ) the pass line bet behind
the pass line
.
If he sometimes seems to approach
the symbolic view
, at
other times he comes very close to a strong realistic doctrine
.
If the late queen would have believed her men
of war as she did her scribes
, we had in her time beaten
that great empire in pieces and made their kings
of figs and oranges as in old
times.
If implemented using remainders
of Euclidean division rather than subtractions
, Euclid's algorithm computes
the GCD
of large numbers efficiently: it never requires more division steps than five
times the number of digits
( base 10
) of the smaller integer
.
If anyone shall violate
the truce
of God he shall
be admonished three
times by the bishop to make satisfaction
.
If one flips a coin 21
times in a row and obtains 21 heads
, one might rationally conclude a high probability
of bias towards heads
, and hence conclude
that future flips
of this coin are also highly likely to
be heads
.
If you are listening carefully to everything I say
, you just heard me say it three
times.

*
If a thief steals a cow
, a sheep
, a donkey
, a pig
, or a goat
, he
will pay ten
times what it
is worth
.
If we neglect
the possibility
of overlapping states
, which
is valid if
the temperature
is high
, then
the number of times we count
each state
is approximately N < nowiki >!</ nowiki >.
If twice or three
times that does not suffice
, then not even
the wealth
of Croesus or
of Persia
will suffice
.
If V
is a formal language
, then V < sub > i </ sub >,
the i-th power
of the set V
, is a shorthand for
the concatenation
of set V with itself i
times.

*
If creatures similar to plesiosaurs lived in
the waters
of the Loch Ness
, they would
be seen very frequently as they would have to surface several
times a day to breathe
.
If the value being sought occurs k
times in
the list
, and all orderings
of the list are equally likely
, the expected
number of comparisons
is
If the picture contains an area
of the same color
, it can
be compressed without loss
by saying " 200 red dots " instead
of " red dot
, red dot
, ...( 197 more
times )..., red dot
.
If the brightness
of the object exceeded
the maximum limit
of eight
times the brightness
of Canopus
, the spacecraft would search for a new star
.
If the force depends on time
, the change in momentum
( or impulse
) between
times and
is
If the IMF has a southward component
, this not only pushes
the magnetopause boundary closer to Earth
( at
times to about half its usual distance ), but it also produces an injection
of plasma from
the tail
, much more vigorous than
the one associated with substorms
.

Saints All-Pro quarterback Drew Brees made a controversial tweet on June 20
, 2012 stating
, "
If NFL fans were told there were " weapons
of mass destruction " enough
times, they'd believe it
.
If the universe
is homogeneous at a large scale
, then there would
be four
times as many stars in a second shell between 2
, 000
, 000
, 000 to 2
, 000
, 000
, 001 light years away
.
0.226 seconds.