query: How to prove this element is strictly positive?
positive_passages.docid: 142145
positive_passages.text: strictly positive elements in $C^*$-algebra
negative_passages.docid: 79452
negative_passages.text: How to prove that it is a group?
negative_passages.docid: 156669
negative_passages.text: Trying to prove a simple (?) inequality
negative_passages.docid: 75211
negative_passages.text: Theorem about positive matrices
negative_passages.docid: 27691
negative_passages.text: How to prove Boole’s inequality
negative_passages.docid: 139011
negative_passages.text: How to prove $B-A \succeq 0 \Leftrightarrow$ ellipsoid $x^TBx \leq 1$ contains $x^TAx \leq 1$?
negative_passages.docid: 16660
negative_passages.text: Prove that any positive number has an $n$th root
negative_passages.docid: 105768
negative_passages.text: Proof involving absolute value and maximums
negative_passages.docid: 109470
negative_passages.text: Proof of whether a specific element is in a commutative, invertible monoid.
negative_passages.docid: 100731
negative_passages.text: Positive operator has a positive spectrum?
negative_passages.docid: 66707
negative_passages.text: How to prove this inequality? $ | z-1 | \le | | z | -1 | + | z| \cdot | \arg z | $
negative_passages.docid: 69012
negative_passages.text: How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?
negative_passages.docid: 114245
negative_passages.text: What might I use to show that an entire function with positive real parts is constant?
negative_passages.docid: 144019
negative_passages.text: A strictly positive operator is invertible
negative_passages.docid: 80255
negative_passages.text: How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
negative_passages.docid: 59280
negative_passages.text: Need help with Proof by Strong Induction question
negative_passages.docid: 32772
negative_passages.text: Proving units in a ring