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What (who) is rock back and forth - definition
A METHOD FOR SHOWING ISOMORPHISM BETWEEN COUNTABLY INFINITE STRUCTURES SATISFYING SPECIFIED CONDITIONS
Back and forth method; Cantor's back and forth method; Back-and-forth property; Cantor back-and-forth method; Cantor's back-and-forth method; Back-and-forth argument
Back-and-forth method
In mathematical logic, especially set theory and model theory, the back-and-forth method is a method for showing isomorphism between countably infinite structures satisfying specified conditions. In particular it can be used to prove that
Back & Forth (EP)
EXTENDED PLAY BY SKINNY PUPPY
Back and Forth (album); Back & Forth (album)
Back & Forth is the self-published debut EP by Skinny Puppy, released in 1984. It was supposed to be a limited edition of 50 copies but only 35 were actually made.
Back and Forth Series Two
COMPILATION ALBUM BY SKINNY PUPPY
Back and Forth Series 2
Back and Forth Series Two is a compilation album by industrial band Skinny Puppy. It consists of the entire Back and Forth release remixed from the original four-track tapes, including raw live recordings and studio rarities.
Wikipedia
Back-and-forth method
In mathematical logic, especially set theory and model theory, the back-and-forth method is a method for showing isomorphism between countably infinite structures satisfying specified conditions. In particular it can be used to prove that
- any two countably infinite densely ordered sets (i.e., linearly ordered in such a way that between any two members there is another) without endpoints are isomorphic. An isomorphism between linear orders is simply a strictly increasing bijection. This result implies, for example, that there exists a strictly increasing bijection between the set of all rational numbers and the set of all real algebraic numbers.
- any two countably infinite atomless Boolean algebras are isomorphic to each other.
- any two equivalent countable atomic models of a theory are isomorphic.
- the Erdős–Rényi model of random graphs, when applied to countably infinite graphs, almost surely produces a unique graph, the Rado graph.
- any two many-complete recursively enumerable sets are recursively isomorphic.
Examples of use of rock back and forth
1. "It was around 2:30pm and the building suddenly began to rock back and forth," one girl who managed to escape said.
2. In the frenetic opening, dancers rock back and forth, stutter and rewind, strain their necks to look to the sky for incoming missiles, while in the final climax, the beatbox battle pins the audience to the back of their seats.
3. His movie houses include leatherette, stadium–style seats that rock back and forth, as well as the "biggest screens we can find." "I‘m already paying a high price to get into the movie and completely insane prices for snacks and popcorn.
4. "We‘re also a nation of immigrants, and we must uphold that tradition." I was reminded of the New Yorker editor who told one writer that he‘d crafted a sentence so exquisitely balanced that if touched ever so lightly, it would "rock back and forth forever." Bush‘s speech was not like any other major address of his presidency.