More recent stories ( post-Crisis ) often feature the general public assuming that Superman has no secret identity due to the fact that he, unlike most heroes, doesn't wear a mask.

Another barrier to reform is assuming that schools are like businesses — when in fact they are very different.

Any hope Oxford might have had of assuming parental care of his daughters was dashed by Sir Robert Cecil, due to the fact that he had never supported them financially in the past, and now had yet another wife and child.

Images which later displayed attributes of both genders are believed to be in accordance with the Lotus Sutra, where Avalokitesvara has the supernatural power of assuming any form required to relieve suffering, and also has the power to grant children ( possibly relating to the fact that in this Sutra, unlike in others, both men and women are believed to have the ability to achieve enlightenment.

In fact, by assuming the Elliott – Halberstam conjecture or a slightly weaker version, they were able to show that there are infinitely many n such that at least two of n, n + 2, n + 6, n + 8, n + 12, n + 18, or n + 20 are prime.

assuming,, and were not instance variables of but were, in fact, methods.

As was shown by Goursat, Cauchy's integral theorem can be proven assuming only that the complex derivative f '( z ) exists everywhere in U. This is significant, because one can then prove Cauchy's integral formula for these functions, and from that deduce these functions are in fact infinitely differentiable.

The difficulty lies in the fact that even though the Coulomb force diminishes with distance as 1 / r², the average number of particles at each distance r is proportional to r², assuming the fluid is fairly isotropic.

Most hypothetical constructions rely on the fact that hydrogen bombs can be made arbitrarily large assuming there are no concerns about delivering them to a target ( see Teller – Ulam design ) or that they can be " salted " with materials designed to create long-lasting and hazardous fallout ( e. g., a cobalt bomb ).

This stems from the fact that a notary is expected to verify the facts, assertions, or events mentioned in his act, thereby assuming liability for and giving warrant to its contents.

A color-blind person who approaches Tipperary Hill, not knowing about the different color pattern at that particular traffic light, could cause a severe accident by seeing the light at the bottom and assuming it is green when it in fact is red, or vice versa.

An example of an application of Markov's inequality is the fact that ( assuming incomes are non-negative ) no more than 1 / 5 of the population can have more than 5 times the average income.

In fact, the most compelling reason for this practice is that the party with the most seats can survive confidence votes so long as the smaller party ( or parties ) simply abstain from confidence votes, whereas a governing party without a plurality in the House needs at least one other party to vote with it at all times ( assuming the largest party will always vote no confidence, but that is almost certain to occur when they are denied the opportunity to govern ).

If we assume that there is in fact no experimentally detectable difference in these " exchange macrostates " available, then using the entropy which results from assuming the particles are indistinguishable will yield a consistent theory.

Mistakenly assuming their ground speed to be faster than it really was, the crew may have deduced that they had already safely crossed the Andes, and so commenced their descent to Santiago, whereas in fact they were still a considerable distance to the east-north-east and were approaching the cloud-shrouded Tupungato Glacier at high speed.

A simpler argument, assuming the knowledge of all the subfields as given by Galois theory, is to note the independence of 1, α, β and αβ over the rationals ; this shows that the subfield generated by γ cannot be that generated α or β, nor in fact that generated by αβ, exhausting all the subfields of degree 2.

However, this resolution is invalid, since the paradox is proved by contradiction: assuming that there is any uninteresting number, we arrive to the fact that that same number is interesting, hence no number can be uninteresting ; its aim is not in particular to identify the interesting or uninteresting numbers, but to speculate whether any number can in fact exhibit such properties.

In fact, Clark himself was taken aback by the apparent scope of his influence on colonial affairs, writing to his wife, “ Governor Kuroda consults me constantly and always follows my advice .” He later wrote, “ I tremble to think how much confidence is reposed in me and what responsibilities I am daily assuming .”

Similar examples can be found with F < sub > 2 </ sub > replaced by any finite field ; the obstructions in a proper formulation of Hypothesis H over F, where F is a finite field, are no longer just local but a new global obstruction occurs with no classical parallel, assuming hypothesis H is in fact correct.

However, on 20 April 2004, he announced in the House of Commons that a referendum would in fact be held, assuming the treaty was accepted by the European Council.

New Frontier greatly fleshes out the character, assuming that she is, in fact, Number One.

It also turns out his obsessive clove-chewing and broken Morporkian are in fact a disguise meant to delude foreigners into falsely assuming he is nothing but an uncivilized barbarian.

When Tommy ( now acting Lieutenant, assuming command after Lou's death ) is told by Needles to type a report on that final incident, it is revealed, from flashbacks while Tommy is filling out a department report, that it was in fact only Lou that died after having his face burned off in the fire.

`` We were possessed by visions of a new civilization to come, very pure and elevated '', he has said, `` in fact some ideal form of socialism such as we had dreamed of since the war of 1914-1918 ''.

The great absorbency of this tissue and the fact that it is easier to control than a sponge makes it an ideal tool for the watercolorist.

There was, however, some suggestion that post dive fatigue is due to sub-clinical decompression sickness ( DCS ) ( i. e. micro bubbles in the blood insufficient to cause symptoms of DCS ); the fact that the study mentioned was conducted in a dry chamber with an ideal decompression profile may have been sufficient to reduce sub-clinical DCS and prevent fatigue in both nitrox and air divers.

In fact, if I is a nonzero ideal of R then any element a of I

From the outset, this new republic held that film would be the most ideal propaganda tool for the Soviet Union because of its widespread popularity among the established citizenry of the new land ; Vladimir Lenin, in fact, declared it the most important medium for educating the masses in the ways, means and successes of Communism, a position which was later echoed by Joseph Stalin.

The support of overscan, interlacing and genlocking capabilities, and the fact that the display timing was very close to broadcast standards ( NTSC or PAL ), made the Amiga the first ideal computer for video purposes, and indeed, it was used in many studios for digitizing video data ( sometimes called frame-grabbing ), subtitling and interactive video news.

For instance, the ring ( in fact field ) of complex numbers, which can be constructed from the polynomial ring R over the real numbers by factoring out the ideal of multiples of the polynomial.

In other words, we are urged to believe that Plato's theory of ideas is an abstraction, divorced from the so-called external world, of modern European philosophy, despite the fact Plato taught that ideas are ultimately real, and different from non-ideal things -- indeed, he argued for a distinction between the ideal and non-ideal realm.

Two or more buffer solutions are used in order to accommodate the fact that the " slope " may differ slightly from ideal.

* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.

Truth is most often used to mean in accord with fact or reality or fidelity to an original or to a standard or ideal.

Many Indian restaurants of the sizeable Thai-Indian community will also have vegetarian dishes on offer, due to the fact that vegetarianism is held as an ideal by many followers of the Hindu faith.

In his writings, Rabbi Kook speaks of vegetarianism as an ideal, and points to the fact that Adam did not partake of the flesh of animals.

Geijer's poem did much to propagate the new romanticised ideal of the Viking, which had little basis in historical fact.

The fact that the vapor is taken to be ideal is the least of our worries.

Since a one sided maximal ideal A is not necessarily two-sided, the quotient R / A is not necessarily a ring, but it is a simple module over R. If R has a unique maximal right ideal, then R is known as a local ring, and the maximal right ideal is also the unique maximal left and unique maximal two-sided ideal of the ring, and is in fact the Jacobson radical J ( R ).

In fact in practice the curtains do not run at a constant speed as they would in an ideal design, obtaining an even exposure time depends mainly on being able to make the two curtains accelerate in a similar manner.

For gases at room temperature, the range of volumetric heat capacities per atom ( not per molecule ) only varies between different gases by a small factor less than two, due to the fact that in every ideal gas has the same molar volume.

This fact gives each gas molecule had the same effective " volume " in all ideal gases ( although this volume / molecule in gases is far larger than molecules occupy on average in solids or liquids ).

In fact, in the general case of a ring, these two requirements define the notion of an ideal in a ring.