例句與造句

1. One such function is the Cantor normal form for surreal numbers.
2. The Cantor normal form provides a standardized way of writing ordinals.
3. Using Cantor normal forms, the ordinals less than ? 0 can be represented by finite rooted trees.
4. Any solution to this equation has Cantor normal form \ varepsilon = \ omega ^ { \ varepsilon }.
5. If \ gamma is less than \ varepsilon _ 0, we use the iterated Cantor normal form of \ gamma.
6. It's difficult to find cantor normal form in a sentence. 用cantor normal form造句挺難的
7. In that case Cantor normal form does not express the ordinal in terms of smaller ones; this can happen as explained below.
8. To compare two ordinals written in Cantor normal form, first compare \ beta _ 1, then c _ 1, then \ beta _ 2, then c _ 2, etc ..
9. A minor variation of Cantor normal form, which is usually slightly easier to work with, is to set all the numbers " c " " i " equal to 1 and allow the exponents to be equal.
10. Another variation of the Cantor normal form is the " base ? expansion ", where ? is replaced by any ordinal ? > 1, and the numbers " c " " i " are positive ordinals less than ?.
11. As discussed above, the Cantor Normal Form of ordinals below \ varepsilon _ 0 can be expressed in an alphabet containing only the function symbols for addition, multiplication and exponentiation, as well as constant symbols for each natural number and for \ omega.
12. Canonicalness can be checked recursively : an expression is canonical if and only if it is either the iterated Cantor normal form of an ordinal less than \ varepsilon _ 0, or an iterated base \ delta representation all of whose pieces are canonical, for some \ delta = \ psi ( \ alpha ) where \ alpha is itself written in iterated base \ Omega representation all of whose pieces are canonical and less than \ delta.