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The product of the x and y values of each point on the curve equals the constant of proportionality (k). Since neither x nor y can equal zero (because k is non-zero), the graph never crosses either axis. Direct and inverse proportion contrast as follows: in direct proportion the variables increase or decrease together.
A proportion is a mathematical statement expressing equality of two ratios. [1] [2]: =: a and d are called extremes, b and c are called means. Proportion can be written as =, where ratios are expressed as fractions.
where denotes direct proportionality. That is, scaling by a constant c {\displaystyle c} simply multiplies the original power-law relation by the constant c − k {\displaystyle c^{-k}} . Thus, it follows that all power laws with a particular scaling exponent are equivalent up to constant factors, since each is simply a scaled version of the ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
The sign of proportionality is not the greek lower case letter alpha (α), but the symbol ∝ (in Arial Unicode MS the symbol is a bit too small, in most type faces it is bigger, as seen in LaTeX: ). In some countries, Sweden for instance, the symbol ∼ {\displaystyle \sim } or ∼ is used instead of ∝.
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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
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