query: Proving a Relation that is a Function by Division Algorithm
positive_passages.docid: 151178
positive_passages.text: Is the relation on integers, defined by $(a,b)\in R\iff a=5q+b$, a function?
negative_passages.docid: 91178
negative_passages.text: chain of divisibility relation
negative_passages.docid: 87740
negative_passages.text: Pigeonhole Principle about division
negative_passages.docid: 147375
negative_passages.text: Prove :(P → Q) ∨ (Q → P) using natural deduction
negative_passages.docid: 13390
negative_passages.text: Recursive Monotone Decreasing Sequence Proof ${x_{k}} = \frac{1}{2}\left({x_{k-1}+\frac{a}{{x_{k-1}}}}\right)$
negative_passages.docid: 145759
negative_passages.text: formal proof from calulus
negative_passages.docid: 33011
negative_passages.text: Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
negative_passages.docid: 53497
negative_passages.text: Prove that the function is continuous and differentiable (not as easy as it sounds imo)
negative_passages.docid: 64437
negative_passages.text: Proof by induction (power rule of the derivative)
negative_passages.docid: 152347
negative_passages.text: Proof that a certain entire function is a polynomial
negative_passages.docid: 155642
negative_passages.text: Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
negative_passages.docid: 78471
negative_passages.text: Closure of $\{\frac{1}{n}\}:=M$
negative_passages.docid: 133498
negative_passages.text: Show that Function Compositions Are Associative
negative_passages.docid: 128446
negative_passages.text: Why polynomial division algorithm works for $x-a$ or any monic polynomial?
negative_passages.docid: 31555
negative_passages.text: Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
negative_passages.docid: 91980
negative_passages.text: Prove that f is one-to-one on D
negative_passages.docid: 1641
negative_passages.text: Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$