query: If $r(t)$ is periodic and non-constant, then there exists a minimal $T$, such that : $r(t+T) = r(t)$.
positive_passages.docid: 158230
positive_passages.text: prove that a non constant periodic, continuous function has a "smallest period"
negative_passages.docid: 109091
negative_passages.text: Why do non-constant periodic functions have no limit at infinity?
negative_passages.docid: 91744
negative_passages.text: Proving sum of sines is periodic when ratio of their frequencies is rational using differentation
negative_passages.docid: 89537
negative_passages.text: $ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
negative_passages.docid: 447
negative_passages.text: Minimal polynomial for T is a product of distinct linear factors
negative_passages.docid: 103485
negative_passages.text: Antiderivative of periodic function
negative_passages.docid: 91398
negative_passages.text: Continuous function on R which tends to infinity on open interval must have a minimum
negative_passages.docid: 143354
negative_passages.text: Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
negative_passages.docid: 99782
negative_passages.text: $a_{n+1}=|a_n|-a_{n-1} \implies a_n \; \text{is periodic}$
negative_passages.docid: 158444
negative_passages.text: Is this periodic solution unique? (ODE)
negative_passages.docid: 102485
negative_passages.text: Showing that a topological space is ${\rm T}_1$
negative_passages.docid: 98824
negative_passages.text: linear transformation $T$ such that $TS = ST$
negative_passages.docid: 103285
negative_passages.text: Limit of a periodic function
negative_passages.docid: 74792
negative_passages.text: $(X,\tau)$ needs to be $T_1$ in order to guarantee that $A'$ is closed?
negative_passages.docid: 126259
negative_passages.text: Minimum of a function on an open interval
negative_passages.docid: 44559
negative_passages.text: Finding a homeomorphism $\mathbb{R} \times S^1 \to \mathbb{R}^2 \setminus \{(0,0)\}$
negative_passages.docid: 132824
negative_passages.text: Does $f$ monotone and $f\in L_{1}([a,\infty))$ imply $\lim_{t\to\infty} t f(t)=0$?