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The following famous example of a nonconstructive proof shows that there exist two irrational numbers a and b such that is a rational number. This proof uses that 2 {\displaystyle {\sqrt {2}}} is irrational (an easy proof is known since Euclid ), but not that 2 2 {\displaystyle {\sqrt {2}}^{\sqrt {2}}} is irrational (this is true, but the proof ...
Scientific evidence. Scientific evidence is evidence that serves to either support or counter a scientific theory or hypothesis, [1] although scientists also use evidence in other ways, such as when applying theories to practical problems. [2] Such evidence is expected to be empirical evidence and interpretable in accordance with the scientific ...
Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles. The unchanged properties are called invariants. In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
The patterns in a climograph describe not just a location's climate but also provide evidence for that climate's relative geographical location. For example, a climograph with a narrow range in temperature over the year might represent a location close to the equator, or alternatively a location adjacent to a large body of water exerting a ...
For other uses, see Consilience (disambiguation). In science and history, consilience (also convergence of evidence or concordance of evidence) is the principle that evidence from independent, unrelated sources can "converge" on strong conclusions. That is, when multiple sources of evidence are in agreement, the conclusion can be very strong ...
Line–line intersection. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line. Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection. In three-dimensional Euclidean geometry, if two lines are not in ...
Statistical proof is the rational demonstration of degree of certainty for a proposition, hypothesis or theory that is used to convince others subsequent to a statistical test of the supporting evidence and the types of inferences that can be drawn from the test scores. Statistical methods are used to increase the understanding of the facts and ...
A multicellular thunderstorm cluster is a thunderstorm that is composed of multiple convective cells, each being at a different stage in the life cycle of a thunderstorm. It appears as several anvils clustered together. A cell is an updraft/downdraft couplet. These different cells will dissipate as new cells form and continue the life of the ...