Examples of using Lemma in English and their translations into Serbian
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Cyrillic
So the lemma is proved.
Thereby proving Zorn's Lemma.
So the Lemma is proven.
Now we need another lemma.
Hence the Lemma is proved.
And that's how we're going to prove our lemma.
Thus, the lemma is proved.
So if I can get them,why can't Lemma?
And thus the lemma is proved.
The lemma reduces to the following simple claim.
Therefore, the lemma is proved.
Lemma 1: Let k be the min cut size, and let C={e1,e2,…,ek} be the min cut.
Further information: Lexeme and Lemma(morphology).
Armed with this lemma I can easily prove the following theorem.
His 1920 proof employed the axiom of choice, but he later(1922 and 1928)gave proofs using Kőnig's lemma in place of that axiom.
By the lemma above, if we keep taking square roots of an- 1, we will get either 1 or- 1.
The most important among them are Zorn's lemma and the well-ordering theorem.
By Euclid's lemma it divides one of the factors x- 1 or x+ 1, implying that x is congruent to either 1 or- 1 modulo pp.
Cramer's rule can be used to prove the Cayley Hamilton theorem of linear algebra,as well as Nakayama's lemma, which is fundamental in commutative ring theory.
A lemma on its own is difficult to solve because the solution changes dependent upon whether or not the subsequent proposition is auxiliary or subsidiary.
This is a joke: although the three are all mathematically equivalent, many mathematicians find the axiom of choice to be intuitive, the well-ordering principle to be counterintuitive,and Zorn's lemma to be too complex for any intuition.
Zorn's lemma: Every non-empty partially ordered set in which every chain(i.e. totally ordered subset) has an upper bound contains at least one maximal element.
To show that one of these must be true, recall Fermat's little theorem, that for a prime number n:a n- 1≡ 1( mod n).{\displaystyle a^{n-1}\equiv 1{\pmod{n}}.} By the lemma above, if we keep taking square roots of an- 1, we will get either 1 or- 1.
The difference between the lemma and the root is that the lemma is the citation form of the word, while the root is the substring of the lemma to which suffixes are added.
The ancient manuscripts invariably refer to a"Laertius Diogenes", and this form of the name is repeated by Sopater[4] and the Suda.[5] The modern form"Diogenes Laertius" is much rarer,used by Stephanus of Byzantium,[6] and in a lemma to the Greek Anthology.[7] He is also referred to as"Laertes"[8] or simply"Diogenes".
The sparsification lemma is proven by repeatedly finding large sets of clauses that have a nonempty common intersection in a given formula, and replacing the formula by two simpler formulas, one of which has each of these clauses replaced by their common intersection and the other of which has the intersection removed from each clause.
The Axiom of Choice is obviously true,the well-ordering principle obviously false, and who can tell about Zorn's lemma?- Jerry Bona This is a joke: although the three are all mathematically equivalent, many mathematicians find the axiom of choice to be intuitive, the well-ordering principle to be counterintuitive, and Zorn's lemma to be too complex for any intuition.
Eulerian matroid, an abstract generalization of Eulerian graphs Five room puzzle Handshaking lemma, proven by Euler in his original paper, showing that any undirected connected graph has an even number of odd-degree vertices Hamiltonian path- a path that visits each vertex exactly once. Route inspection problem, search for the shortest path that visits all edges, possibly repeating edges if an Eulerian path does not exist.