democritus discovered that everything is made of atoms.
democritus discovered that everything is made of atoms.
who discovered that everything is made of atoms?
democritus
he then proposes relative weights for the atoms of a few elements, without going into further detail.









































the main points of dalton's atomic theory, as it eventually developed, are:









































bullet::::1. elements are made of extremely small particles called atoms.









































bullet::::2. atoms of a given element are identical in size, mass and other properties; atoms of different elements differ in size, mass and other properties.









































bullet::::3. atoms cannot be subdivided, created or destroyed.









































bullet::::4. atoms of different elements combine in simple whole-number ratios to form chemical compounds.









































bullet::::5. in chemical reactions, atoms are combined, separated or rearranged.
john dalton
base case |"atoms"(φ) − "atoms"(ψ)| = 0: in this case, φ is suitable. this is because since |"atoms"(φ) − "atoms"(ψ)| = 0, we know that "atoms"(φ) ⊆ "atoms"(φ) ∩ "atoms"(ψ). moreover we have that ⊨φ → φ and ⊨φ → ψ. this suffices to show that φ is a suitable interpolant in this case.









































let’s assume for the inductive step that the result has been shown for all χ where |"atoms"(χ) − "atoms"(ψ)| = n. now assume that |"atoms"(φ) − "atoms"(ψ)| = n+1. pick a "q" ∈ "atoms"(φ) but "q" ∉ "atoms"(ψ). now define:









































φ' := φ[⊤/"q"] ∨ φ[⊥/"q"]
craig interpolation