Without this restriction, bizarre maps ( using regions of finite area but infinite perimeter ) can require more than four colors.

Without any such logical operators of valence 0, these two constants can only be expressed using quantifiers.

Without first finding the radian frequency, the natural frequency can be found directly using:

Without using overscan, the Amiga's graphics display is 320 or 640 pixels wide by 200 ( NTSC ) or 256 ( PAL ) pixels tall.

Without using measures of income adjusted for inflation, they will tend to overstate the effects of economic growth.

Without copying any one historical model, and without compromising its authentic stone-on-stone construction by using modern steel girders, Saint John the Divine is an example of the 13th century High Gothic style of northern France.

The use of phonics in American education dates at least to the work of Favell Lee Mortimer, whose works using phonics includes the early flashcard set Reading Disentangled ( 1834 ) and text Reading Without Tears ( 1857 ).

* Without using RMTI, Hop count can not exceed 15, in the case that it exceeds this limitation, it will be considered invalid.

* Without using RMTI, RIP has slow convergence and count to infinity problems.

Without actually accusing the group of using the hashish drug, the Caliph used the term in a pejorative manner.

Without using countable choice, it is not possible to constructively prove the fundamental theorem of algebra for complex numbers based on the Dedekind real numbers ( which are not constructively equivalent to the Cauchy real numbers without countable choice < ref > For the minimum necessary to prove their equivalence, see Bridges, Schuster, and Richman ; 1998 ; < cite > A weak countable choice principle </ cite >; available from .</ ref >).

Without an extra Global navigation satellite system, receiver tracking is difficult, but not impossible, as the position of a mobile unit can be determined using a Doppler shift calculation from the satellite.

Without analyzing the statistical uncertainty of a given 100-year flood, scientists and engineers can decrease the uncertainty by using two practical rules.

Without warning, in 2000 French urban climber Alain " Spiderman " Robert, using only his bare hands, climbing shoes and no safety devices, scaled the obelisk all the way to the top.

Without using an IF, all the complicated filters and detectors in a radio or television would have to be tuned in unison each time the frequency was changed, as was necessary in the early tuned radio frequency receivers.

Without using their considerable hydropower output, silver mining in the Harz would never have been able to attain its major economic significance.

Without these local organizations pushing for their rights and, many times, using self-defense tactics, not much would have changed, according to scholars such as Hill.

Without the time or resources to build sufficient aircraft and train experienced pilots, the surviving Japanese carriers were mere shadows of their former selves, a fact the Japanese recognized by using them as sacrificial decoys at Leyte Gulf.

Kean has also been criticized for using his role as the chairman of the 9 / 11 Commission in order to make profit, such as his book, Without Precedent.

* Without taking more water, wipe your hair from the middle down to the forehead, or vice versa, using the index finger of your right hand ; it is mustahab to use three fingers.

Without the software installed, the F keys will do nothing, and toggling them back to normal by using the F Lock has been found by some to be unreliable as the keyboard will often randomly and inexplicably " untoggle " the F Lock key.

Without all-seeing devices like radar, a pilot could approach his foe stealthily, using clouds, haze or even using the enemy aircraft's own wings or tail to conceal his approach.

Without a case to provide these functions, caseless rounds using nitrocellulose will begin to cook off, firing from the residual chamber heat, much sooner than metal cased cartridges would.

Though used earlier in papers and discussions, the term 4GL was first used formally by James Martin in his 1982 book Applications Development Without Programmers to refer to non-procedural, high-level specification languages.

A curriculum-free philosophy of homeschooling may be called unschooling, a term coined in 1977 by American educator and author John Holt in his magazine Growing Without Schooling.

Without an article, the term can refer to the entirety of humanity ( also: " society in general ", " society at large ", etc.

Without a normal gene to provide normal proteins in addition to the abnormal proteins caused by a MECP2 mutation, the XY karyotype male fetus is unable to check the development of the disease, hence the failure of many male fetuses with a MECP2 mutation to survive to term.

The term " unschooling " probably derives from Ivan Illich's term " deschooling ", and was popularized through John Holt's newsletter Growing Without Schooling.

Without creating a school in the strict sense of the term, Wieland had a strong influence on the German literature of his time.

Without accusing the group of utilizing the hashish drug, the caliph used the term in a pejorative manner.

Black Market Music did not receive the same level of long term recognition and media hype as Without You I'm Nothing did, but its peak sales outperformed those of its predecessor in both the UK and France.

This term is heard in " Brooklyn Without Limits ", a 2010 episode of the comedy 30 Rock.

Taiji ( literally " great pole ") is a Chinese cosmological term for the " Supreme Ultimate " state of undifferentiated absolute and infinite potentiality, contrasted with the Wuji ( 無極, " Without Ultimate ").

Without caps there is a risk that teams will overspend in order to win now at the expense of long term stability.

The term cruelty-free was first used in this way by Lady Dowding who persuaded manufacturers of fake furs to use the label Beauty Without Cruelty and went on to found the charity Beauty Without Cruelty in 1959.

Without giving it much thought, he used the term as the title of his talk.

Without qualifications, the term " digital image " usually refers to raster images also called bitmap images.

Without a qualifier, the term ejection fraction basically refers to the blood output of the left ventricle.

The term " natural childbirth " was coined by obstetrician Grantly Dick-Read upon publication of his book Natural Childbirth in the 1930s, which was followed by the 1942 Childbirth Without Fear.

Throughout his 1935 travel book Journey Without Maps, British author Graham Greene uses " piccaninny " as a general term for African children.

The French expert on Indochina and Vietnam, Bernard Fall, who wrote Street Without Joy, said that " revolutionary warfare " ( guerrilla warfare plus political action ) might be a more accurate term to describe small wars such as insurgencies.

Without the dam, the long term costs for people would be much greater and lack of an income source for future generations would put increasing pressure on the environment.

In the short term, the prohibition was of limited effect ; as late as 1648, the Red Bull hosted a performance of Fletcher's Wit Without Money ; advertisements for the performance were thrown into gentlemen's carriages.

The machine has been dubbed AWOL, a play on the military term AWOL, Absent Without Leave.