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2. Completeness of the real numbers - Wikipedia

   en.wikipedia.org/wiki/Completeness_of_the_real...

   The least-upper-bound property states that every nonempty subset of real numbers having an upper bound (or bounded above) must have a least upper bound (or supremum) in the set of real numbers. The rational number line Q does not have the least upper bound property. An example is the subset of rational numbers

3. Complete set of invariants - Wikipedia

   en.wikipedia.org/wiki/Complete_set_of_invariants

   In the classification of two-dimensional closed manifolds, Euler characteristic (or genus) and orientability are a complete set of invariants. Jordan normal form of a matrix is a complete invariant for matrices up to conjugation, but eigenvalues (with multiplicities) are not.

4. Plumbing fixture - Wikipedia

   en.wikipedia.org/wiki/Plumbing_fixture

   The most common plumbing fixtures are: Bathtubs; Bidets; Channel drains; Drinking fountains; Showers; Sinks; Tap (connections for water hoses) . Tapware - an industry term for that sub-category of plumbing fixtures consisting of tap valves, also called water taps (British English) or faucets (American English), and their accessories, such as water spouts and shower heads.

5. Celebrity couples celebrate Valentine's Day: Michelle Obama ...

   www.aol.com/celebrity-couples-celebrate...

   The royals have been married since 2011 and share three children: George, 11, Charlotte, 9, and Louis, 6. Prince William kisses Princess Kate in rare intimate post for Valentine's Day. Michelle ...

6. Feeding a Super Bowl party will cost about the same ... - AOL

   www.aol.com/feeding-super-bowl-party-cost...

   Celebrating football’s biggest game can bring big appetites. Buying Super Bowl fixings this year will cost about the same as last year, but the prices of individual products may seesaw ...

7. Shower - Wikipedia

   en.wikipedia.org/wiki/Shower

   Fixed shower heads: Traditional fixed shower-heads are mostly common shower-faucets because they can easily connect to the plumbing fixtures without any additional hardware. Shower handsets/ bidet shower : Hand-set shower-faucets are connected by a flexible hose, and can also be mounted and used like a fixed shower-head.

8. Mortgage and refinance rates for Jan. 15, 2025: Rates rise ...

   www.aol.com/finance/mortgage-and-refinance-rates...

   See today's average mortgage rates for a 30-year fixed mortgage, 15-year fixed, jumbo loans, refinance rates and more — including up-to-date rate news.

9. Total set - Wikipedia

   en.wikipedia.org/wiki/Total_set

   In functional analysis, a total set (also called a complete set) in a vector space is a set of linear functionals with the property that if a vector satisfies () = for all , then = is the zero vector.