query: Prove $[0, 1]$ and $(0, 1]$ are equinumerous
positive_passages.docid: 22869
positive_passages.text: Prove $[0, 1]$ and $(0, 1]$ are equinumerous by use of bijection
negative_passages.docid: 106884
negative_passages.text: Is there a continuous bijection between an interval $[0,1]$ and a square: $[0,1] \times [0,1]$?
negative_passages.docid: 13398
negative_passages.text: Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
negative_passages.docid: 122076
negative_passages.text: A one line proof that one is zero using Mathematica 10
negative_passages.docid: 70304
negative_passages.text: Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
negative_passages.docid: 45216
negative_passages.text: Cardinality of $[0,1]$
negative_passages.docid: 143586
negative_passages.text: Is $[0,1]$ a union of family of disjoint closed intervals?
negative_passages.docid: 135469
negative_passages.text: Showing Equality of Winding Numbers
negative_passages.docid: 61640
negative_passages.text: Prove c exists for f:[0,1] -> R
negative_passages.docid: 29065
negative_passages.text: Encode each $n_1,n_2,n_3,...∈N^N$ by an inﬁnite sequence of 0s and 1s with inﬁnitely many 0s, and give a proof that $N^N$ is equinumerous with $R$.
negative_passages.docid: 110464
negative_passages.text: Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
negative_passages.docid: 15000
negative_passages.text: Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
negative_passages.docid: 7003
negative_passages.text: Inductive proof of a formula for Fibonacci numbers
negative_passages.docid: 35313
negative_passages.text: Proof of Euclid's Lemma
negative_passages.docid: 133884
negative_passages.text: A proof using Yoneda lemma
negative_passages.docid: 92583
negative_passages.text: Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
negative_passages.docid: 111756
negative_passages.text: How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?