Venn diagram with increasing numbers of sides. They are also two-dimensional representations of hypercubes. Henry John Stephen Smith devised similar "n"-set diagrams using sine curves with the series of equations Charles Lutwidge Dodgson (aka Lewis Carroll) devised a five-set diagram known as Carroll's square. Joaquin and Boyles, on the other hand, proposed supplemental rules for the standard Venn diagram in able to account for certain problem cases. For instance, regarding the issue of representing singular statements, they suggest to consider the Venn diagram circle as a representation of a set of things, and use first-order logic and set theory to treat categorical
Pen name may use different pen names for each, sometimes with no attempt to conceal a true identity. Romance writer Nora Roberts writes erotic thrillers under the pen name J. D. Robb (such books are titled "Nora Roberts writing as J. D. Robb"); Scots writer Iain Banks wrote mainstream or literary fiction under his own name and published science fiction under Iain M. Banks; Samuel Langhorne Clemens used the aliases Mark Twain and Sieur Louis de Conte for different works. Similarly, an author who writes both fiction and non-fiction (such as the mathematician and fantasy writer Charles Dodgson, who wrote as Lewis