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Examples of such spaces include the Cantor space and Baire space. Hausdorff zero-dimensional spaces are precisely the subspaces of topological powers where = {,} is given the discrete topology. Such a space is sometimes called a Cantor cube.
Ordered geometry is a form of geometry featuring the concept of intermediacy (or "betweenness") but, like projective geometry, omitting the basic notion of measurement. Ordered geometry is a fundamental geometry forming a common framework for affine , Euclidean , absolute , and hyperbolic geometry (but not for projective geometry).
In the zeroth-order example above, the quantity "a few" was given, but in the first-order example, the number "4" is given. A first-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a linear approximation, straight line with a slope: a polynomial of degree 1.
0th-order contact if the curves have a simple crossing (not tangent). 1st-order contact if the two curves are tangent. 2nd-order contact if the curvatures of the curves are equal. Such curves are said to be osculating. 3rd-order contact if the derivatives of the curvature are equal. 4th-order contact if the second derivatives of the curvature ...
0th or zeroth, an ordinal for the number 0; 0th dimension, a topological space; 0th element, of a data structure in computer science; 0th law of Thermodynamics; Zeroth (software), deep learning software for mobile devices
However, sometimes one uses more than one principal base set. For example, two-dimensional projective geometry may be formalized via two base sets, the set of points and the set of lines. Moreover, a striking feature of projective planes is the symmetry of the roles played by points and lines.
The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes. There are two canonical proofs that are always used to show non-mathematicians what a mathematical proof is like:
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Geometry is one of the oldest mathematical sciences.