Sanakirja.org

Esimerkit

• 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.
• 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.
• 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 - Carl Schurz
• Let \mathbb{Z} be the ring of integers and let 2\mathbb{Z} be its ideal of even integers. Then the quotient ring \mathbb{Z} / 2\mathbb{Z} is a Boolean ring.
• The product of two ideals \mathfrak{a} and \mathfrak{b} is an ideal \mathfrak{a b} which is a subset of the intersection of \mathfrak{a} and \mathfrak{b}. This should help to understand why maximal ideals are prime ideals. Likewise, the union of \mathfrak{a} and \mathfrak{b} is a subset of \mathfrak{a + b}.