Quantifiers
... validity, we should be able to make this into a test for FO invalidity as follows: Have the procedure test for validity. If it is valid, then eventually the procedure will say it is valid (e.g. it says “Yes, it’s valid”), and hence we will know (because the procedure is sound) that it is not invalid ...
... validity, we should be able to make this into a test for FO invalidity as follows: Have the procedure test for validity. If it is valid, then eventually the procedure will say it is valid (e.g. it says “Yes, it’s valid”), and hence we will know (because the procedure is sound) that it is not invalid ...
Rubik's family cubes of all sizes
The original Rubik's cube was a mechanical 3x3x3 cube puzzle invented in 1974 by the Hungarian sculptor and professor of architecture Erno Rubik. Extensions of the Rubik's cube have been around for a long time and come in both hardware and software forms. The major extension have been the availability of cubes of larger size and the availability of the more complex cubes with marked centres. The properties of Rubik’s family cubes of any size together with some special attention to software cubes is the main focus of this article. Many properties are mathematical in nature and are functions of the cube size variable.