Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Mon, 28 Oct 2024 18:23:01 -0700 Received: from [192.168.123.254] (port=33638 helo=jiten.lojban.org) by 4f8f24ca47b9 with smtp (Exim 4.96) (envelope-from ) id 1t5awl-0003nO-0L for jbovlaste-admin@lojban.org; Mon, 28 Oct 2024 18:23:01 -0700 Received: by jiten.lojban.org (sSMTP sendmail emulation); Tue, 29 Oct 2024 01:22:58 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Added At Word mai'u'au -- By krtisfranks Date: Tue, 29 Oct 2024 01:22:58 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: -1.0 (-) X-Spam_score: -1.0 X-Spam_score_int: -9 X-Spam_bar: - In jbovlaste, the user krtisfranks has added a definition of "mai'u'au" in the language "English". New Data: Definition: unary mekso operator: parity of function; if the input is a unary real-valued function $X_1$ which is defined on a subset of the reals, then the output is $1$ is $X_1$ is even, $-1$ if $X_1$ is odd, and $0$ otherwise. Notes: Let $f$ be a unary function which maps a subset of the reals to the reals; then $f$ is even iff $f(-x) = f(x)$ for all $x$ which belong to the domain of $f$, and $f$ is odd iff $f(-x) = -f(x)$ for all $x$ which belong to the domain of $f$; for such $f$, it is possible for $f$ to be both even and odd (in which case it maps valid inputs uniformly to $0$) and it is possible for $f$ to be neither even nor odd (even if its domain is symmetric over $0$). For other types of functions, this word may be defined, so long as the definition is consistent with restrictions to the aforespecified domain and codomain. See also: "{mai'u}". Jargon: Gloss Keywords: Word: parity of function, In Sense: Word: function parity, In Sense: Place Keywords: You can go to to see it.