例句與造句

1. I defined infinite collection of formulas whose overall meaning is that there is a Collatz sequence that do not reach to 1.
2. It uses no halting symbol, but halts on any word of length less than 2, and computes a slightly modified version of the Collatz sequence.
3. For example, Peano arithmetic is able to prove by induction on " k " that the number 2 k must have a Collatz sequence that ends in 1.
4. :Never mind-I have just realised that these are essentially the same as Collatz sequences if we replace " n " with & minus; " n " . talk ) 11 : 37, 15 February 2009 ( UTC)
5. The Collatz conjecture equivalently states that this tag system, with an arbitrary finite string of " a "'s as the initial word, eventually halts ( see " Tag system # Example : Computation of Collatz sequences " for a worked example ).
6. It's difficult to find collatz sequence in a sentence. 用collatz sequence造句挺難的
7. *PM : Collatz sequences starting with numbers of the form 3n + 1 for odd n < 334, id = 8944 new !-- WP guess : Collatz sequences starting with numbers of the form 3n + 1 for odd n < 334-- Status:
8. *PM : Collatz sequences starting with numbers of the form 3n + 1 for odd n < 334, id = 8944 new !-- WP guess : Collatz sequences starting with numbers of the form 3n + 1 for odd n < 334-- Status:
9. In the model you constructed above, the relevant Collatz sequence " does " actually reach 1 ( or can be assumed to, at least ), but the number of steps needed is a nonstandard natural number .  J . 11 : 06, 2 October 2009 ( UTC)
10. Since the Collatz sequence is computable, you can actually formulate the Collatz conjecture as a single sentence ( \ Pi ^ 0 _ 2 in fact ) in the language of arithmetic by the usual G鰀el-style coding tricks, but then your compactness argument will not work ( precisely because it is a single sentence ).
11. f . that is, according to the compactness thaorem there is a model that hold for P in all of Q formulas and espcially it hold for all Peiano axioms P, and it contain countable sequence of constants of which no one = 1 and constitute Collatz sequence .-- talk ) 10 : 12, 2 October 2009 ( UTC)
12. :: : The problem is that the Collatz conjecture is of the form " for every natural number " a ", there is a finite sequence & tau; of natural numbers such that & phi; ( a, & tau; ) holds and & tau; ends with 1 ", where & phi; is the formula that says & tau; is the Collatz sequence for " a ".
13. These include primes, pseudoprimes, graph colorings, Euler numbers, continued fractions, Stirling numbers, Pythagorean triples, Ramsey theory, Lucas-Bernoulli numbers, quadratic residues, higher-order recurrence sequences, nonlinear recurrence sequences, combinatorial proofs of number-theoretic identities, Diophantine equations, special matrices and determinants, the Collatz sequence, public-key crypto functions, elliptic curves, fractal dimension, hypergeometric functions, Fibonacci polytopes, geometry, graph theory, music, and art.