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Mathematics
Sannon's entropy
Shannon's entropy, \(H(X) = -\sum_{x \in \mathbf{X}} p(x) \log p(x)\), measures how informative the mass function \(p\) is about the occurrence of the possible values of variable \(X\).
Mathematics
The integral definition of the exponential function
The exponential function to the natural base, \(e^x\), can be defined in more than one way. One of them makes use of the integral \(\int_1^{e^x} \frac{dy}{y}= x\).
Physics
Einstein's field equations in general relativity
In Einstein's general relativity, the field equation \(\mathcal{G} = - \frac{8\pi G}{c^4} \mathcal{T}\) relates spacetime curvature (\(\mathcal{G}\)) to its mass-energy content (\(\mathcal{T}\)).