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Homelength function

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# length function

Let $G$ be a group. A length function on $G$ is a function $L\colon G\to\mathbb{R}^{+}$ satisfying:

$\displaystyle L(e)$ | $\displaystyle=$ | $\displaystyle 0,$ | ||

$\displaystyle L(g)$ | $\displaystyle=$ | $\displaystyle L(g^{{-1}}),\quad\forall g\in G,$ | ||

$\displaystyle L(g_{1}g_{2})$ | $\displaystyle\leq$ | $\displaystyle L(g_{1})+L(g_{2}),\quad\forall g_{1},g_{2}\in G.$ |

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## Recent Activity

Apr 22

new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

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new image: information-theoretic-distributed-measurement-dds.png by rspuzio

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Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

Apr 20

new image: information-theoretic-distributed-measurement-dds.png by rspuzio

new image: information-theoretic-distributed-measurement-4.2 by rspuzio

new image: information-theoretic-distributed-measurement-4.1 by rspuzio

new image: information-theoretic-distributed-measurement-3.2 by rspuzio

new image: information-theoretic-distributed-measurement-3.1 by rspuzio

new image: information-theoretic-distributed-measurement-2.1 by rspuzio

Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia