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...them all together. The idea is that it is possible to add the [[infinite]] number of derivatives and come up with a single [[finite]] sum. ...t. He believed that it would be impossible to add an [[infinity|infinite]] number of values and get a single [[finite]] value as a result. ...

...algorithms (also called communication protocols here) are measured by the number of bits communicated between Alice and Bob. ...input string <math>x\in\{0,1\}^n</math> as the binary representation of a number, let <math>\mathrm{FING}(x)=x\bmod p</math> for some random prime <math>p</ ...

| √x is a number whose square is x. | The golden ratio is an [[irrational number]] equal to (1+√5)÷2 or approximately 1.6180339887. ...

...the <math>n</math> properties. We write <math>\bar{A_i}=U-A_i</math>. The number of objects without any of the properties <math>A_1,A_2,\ldots,A_n</math> is ...1,A_2,\ldots,A_n</math> be a family of subsets of <math>U</math>. Then the number of elements of <math>U</math> which lie in none of the subsets <math>A_i</m ...

...the <math>n</math> properties. We write <math>\bar{A_i}=U-A_i</math>. The number of objects without any of the properties <math>A_1,A_2,\ldots,A_n</math> is ...1,A_2,\ldots,A_n</math> be a family of subsets of <math>U</math>. Then the number of elements of <math>U</math> which lie in none of the subsets <math>A_i</m ...

...the <math>n</math> properties. We write <math>\bar{A_i}=U-A_i</math>. The number of objects without any of the properties <math>A_1,A_2,\ldots,A_n</math> is ...1,A_2,\ldots,A_n</math> be a family of subsets of <math>U</math>. Then the number of elements of <math>U</math> which lie in none of the subsets <math>A_i</m ...

...the <math>n</math> properties. We write <math>\bar{A_i}=U-A_i</math>. The number of objects without any of the properties <math>A_1,A_2,\ldots,A_n</math> is ...1,A_2,\ldots,A_n</math> be a family of subsets of <math>U</math>. Then the number of elements of <math>U</math> which lie in none of the subsets <math>A_i</m ...

...the <math>n</math> properties. We write <math>\bar{A_i}=U-A_i</math>. The number of objects without any of the properties <math>A_1,A_2,\ldots,A_n</math> is ...1,A_2,\ldots,A_n</math> be a family of subsets of <math>U</math>. Then the number of elements of <math>U</math> which lie in none of the subsets <math>A_i</m ...

...charge of the atom's nucleus, <math>n \ </math> is the [[principal quantum number]], ''e'' is the charge of the electron, <math> h </math> is [[Planck's cons The Rydberg levels depend only on the principal quantum number <math>n \ </math>. ...

The basic theory, widely agreed, is that highly conserved DNA sequences must have functional ...ment. As can be seen from this alignment, these two [[proteins]] contain a number of conserved amino acid sequences (represented by identical letters aligned ...

...inite]] number of elements. It is less intuitive for sets with an infinite number of elements. The example below uses two of the simplest infinite sets, that of [[natural number]]s, and that of positive [[fraction (mathematics)|fractions]]. The idea is ...

...t the reactivity was independent of the polymer's size. He showed that the number of polymer chains present decreased with size [[Exponential function|expone ...n of compounds with more than two functional groups. He also developed the theory of polymer networks or [[gels]]. ...

The chromatic number of a graph is the minimum number of colors with which the graph can be ''properly'' colored. {{Theorem|Definition (chromatic number)| ...

The chromatic number of a graph is the minimum number of colors with which the graph can be ''properly'' colored. {{Theorem|Definition (chromatic number)| ...

...input string <math>x\in\{0,1\}^n</math> as the binary representation of a number from <math>[2^n]</math>, let <math>\mathrm{FING}(x)=x\bmod p</math> for som The number of bits to be communicated is <math>O(\log k)</math>. We then bound the pr ...

{{Theorem|Hall's Theorem (graph theory form)| ...artite graph, the maximum number of edges in a matching equals the minimum number of vertices in a vertex cover. ...

{{Theorem|Hall's Theorem (graph theory form)| ...artite graph, the maximum number of edges in a matching equals the minimum number of vertices in a vertex cover. ...

== Principles in probability theory == * '''Basics of probability theory''': probability space, events, the union bound, independence, conditional p ...

== Principles in probability theory == * '''Basics of probability theory''': probability space, events, the union bound, independence, conditional p ...

.../math>. The time complexity of fastest matrix multiplication algorithm (in theory) is <math>O(n^{2.376})</math>, and so is the time complexity of this method For multi-variate <math>Q</math>, we prove by induction on the number of variables <math>n</math>. ...