# residuum

## English

### Etymology

From Latin residuum.

### Pronunciation

• IPA(key): /ɹɛˈzɪ.dju.ʌm̩̩/

### Noun

residuum (plural residua)

1. The residue, remainder or rest of something
2. (chemistry) The solid material remaining after the liquid in which it was dissolved has been evaporated; a residue.
3. (fuzzy logic) A binary function from [0,1] × [0,1] to [0,1] which is defined in terms of the t-norm as follows: $x \rightarrow y = \sup \{ z | z * x \leqslant y\}$, where $*$ denotes the t-norm function and $\sup$ denotes the supremum.
The residuum of the minimum t-norm is a function $\rightarrow$ such that $x \rightarrow y = \begin{cases} y, & \text{if } x > y \\ 1, & \text{if } x \leqslant y .\end{cases}$
4. (law) The residue of an estate