Noun

Ideals are like stars; you will not succeed in touching them with your hands. But like the seafaring man on the desert of waters, you choose them as your guides, and following them you will reach your destiny -

If (1) the empty set were called a "small" set, and (2) any subset of a "small" set were also a "small" set, and (3) the union of any pair of "small" sets were also a "small" set, then the set of all "small" sets would form an ideal .

Let $\backslash mathbb\{Z\}$ be the ring of integers and let $2\backslash mathbb\{Z\}$ be its ideal of even integers. Then the quotient ring $\backslash mathbb\{Z\}\; /\; 2\backslash mathbb\{Z\}$ is a Boolean ring.

The product of two ideals $\backslash mathfrak\{a\}$ and $\backslash mathfrak\{b\}$ is an ideal $\backslash mathfrak\{a\; b\}$ which is a subset of the intersection of $\backslash mathfrak\{a\}$ and $\backslash mathfrak\{b\}$. This should help to understand why maximal ideals' are prime ' ideals . Likewise, the union of $\backslash mathfrak\{a\}$ and $\backslash mathfrak\{b\}$ is a subset of $\backslash mathfrak\{a\; +\; b\}$.

Noun

In the soul / Are many lesser faculties, that serve / Reason as chief. Among these fancy next / Her office holds.

How now, my lord! why do you keep alone, / Of sorriest fancies your companions making?

I have always had a fancy that learning might be made a play and recreation to children.

I had a fancy to learn to play the flute.

He took a fancy to her.

to fit your fancies to your father's will

Trainspotting is the fancy of a special lot.

the cat fancy

He fell out of favor with the boxing fancy after the incident.

a great book sale in London, which had congregated all the fancy

London pride is a pretty fancy for borders.

(Shakespeare)

When you have mastered plainsies, the regular jack game, and have learned all the rules, you will be ready to use this part of the book. A fancy is a variation of plainsies which usually requires more skill than plainsies does.

When you get good at jacks, try adding a fancy . A fancy is an extra round at the end of a game. It makes the game a little harder. Jack Be Nimble, Around the World, or Black Widow are some fancies.