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[1] [2] [3] By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers ; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets [ 4 ] (finite sets or sets with ...
, is a triangle-free graph, in which every vertex has exactly three neighbors (a cubic graph). Among all such graphs, it is the smallest. Among all such graphs, it is the smallest. Therefore, it is the (3,4)-cage , the smallest graph that has three neighbors per vertex and in which the shortest cycle has length four.
The files are then exported in PDF 1.3 format according to the file header. When taking a screenshot under Mac OS X versions 10.0 through 10.3, the image was also captured as a PDF; later versions save screen captures as a PNG file, though this behavior can be set back to PDF if desired.
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is denoted mathematically as 3 {\textstyle {\sqrt {3}}} or 3 1 / 2 {\displaystyle 3^{1/2}} . It is more precisely called the principal square root of 3 to distinguish it from the negative number with the same property.
Thus a truecolor PNG is typically larger than a color-reduced GIF, although PNG could store the color-reduced version as a palettized file of comparable size. Conversely, some tools, when saving images as PNGs, automatically save them as truecolor, even if the original data use only 8-bit color, thus bloating the file unnecessarily. [ 56 ]
Steyler Verl., Nettetal 1996, 231-258, ISBN 3-8050-0380-3. - ibidem in: Verbum SVD 37:1-2 (1996) 231-258. Frank Mihalic: Readings in PNG Mission History. A chronicle of SVD and SSpS mission involvement on mainland New Guinea between 1946 and 1996, Divine Word University Press, Madang, PNG 1999, 304 S., ISBN 0-86935-063-3.