ihanteellinen englanniksi | visionary, ideal |

*: Or lull to rest the visionary maid.

*: The visionary hour / When musing midnight reigns.

: a visionary scheme or project

: *rfquotek|Jonathan Swift*

*: There will always be a wide interval between practical and ideal excellence.

*: The idea of ghosts is ridiculous in the extreme; and if you continue to be swayed by ideal terrors —

*: Life and death appeared to me ideal bounds, which I should first break through, and pour a torrent of light into our dark world.

: the ideal theory or philosophy

: ideal point

: An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle.

: 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 - [[w:Carl Schurz|Carl Schurz]]

: 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 $\backslash mathfrak\{a\; +\; b\}$.

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