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Is matter infinitely divisible or not ?

what do you think and what is your general philosophical/theological background ? curious if religious people have a different opinion about this
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No, matter is not infinitely divisible. Molecules and atoms are the smallest units of the substances we are familiar with; quarks are the smallest units that make up the particles of which atoms are composed.

We can detect if particles have smaller subunits by smashing them together and seeing what scatters and how. Electrons behave like perfect point particles; protons don't. But the quark constituents of protons do.