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The Greeks (aka Democritus) had this idea that if you kept dividing something to become smaller and smaller and smaller, eventually you would reach a limit as to how small something could get. Eventually, he said, you would reach a size so small that it could no longer be divided ("atomos" = indivisible.)
Dalton backed that up by actually creating a scientific model for the atom through experimentation, which Democritus was never able to do because the technology was not advanced enough. Dalton agreed with Democritus' ideas, but expanded them to include:
-the idea that things can be broken down into elements
-the definition that elements are atoms with different masses
-compounds are combinations of elements.
So basically he took what Democritus intuited and turned it into an actual model based on scientific theory. One of the main differences between them, besides the fact that Dalton's model was more extensive and complete, is that Dalton backed up his work with experimentation and scientific modeling to come up with a set of axioms, while Democritus focused on defining the concept of an "atom."