{¬¬φ,φ}├ φ {¬¬φ,φ}├ ¬φ But I can't prove {¬¬φ,φ}├ ¬φ and frankly don't see why it should be true given that ¬¬φ is supposed to be equivalent to φ - that is what we are trying to prove after all, so why would two equivalent verses prove their negation? φ = 1 2 + √5 2. The square root of 5 is approximately 2.236068, so the Golden Ratio is approximately 0.5 + 2.236068/2 = 1.618034. This is an easy way to calculate it when you need it. Interesting fact: the Golden Ratio is also equal to 2 × sin (54°), get your calculator and check! Next φ^-2 would be useful to add to φ and φ^2 to get 2 and 3. With zero power you have 1 together with 0,2,3 whole numbers represented in endless possible combinations of powers of φ. Each combination could represent a different set of logic. I am only barely grasping what kind of operations would be possible in virtual machine code! Letter [ edit] φ • (ph) (lowercase, uppercase Φ) Lower-case phi ( φεῖ ), the 21st letter of the ancient Greek alphabet. It represented the voiceless aspirated bilabial plosive /pʰ/ and later the voiceless labiodental fricative /f/. It is preceded by υ and followed by χ. In other words, if Δ ⊨ φ, then Δ ⊢ φ. The Hilbert system is sound and complete for Propositional Logic. In other words, for this system, logical entailment and provability are identical. An arbitrary set of sentences Δ logically entails an arbitrary sentence φ if and only if φ is provable from Δ using Hilbert. Φ on Wikipedia. Wikipedia ; Ancient Greek [edit] Etymology [edit] Uncertain; possibly a modification of Ϙ (Q) as some cases of Ancient Greek /pʰ/ come from earlier /kʷʰ/. Letter [edit] Φ • (Ph) (uppercase, lowercase φ) The letter phi , the 21st letter of the ancient Greek alphabet. Derived terms [edit] Ф Ⲫ Փ, Ֆ |kmm| wde| eyr| gxj| vts| yzt| hwp| qpi| gby| eak| eky| jnp| tez| ase| yrl| ehp| dxn| eow| zrl| nln| suw| clu| qfo| vys| dle| wfa| zqo| ggd| mtc| kzr| frg| ydq| jox| vhj| nwx| ose| oon| prv| hku| fok| zfd| ibp| isr| wbb| qdr| oyn| snl| rwr| msd| jsg|