If the number of logically independent atomic states of affairs is finite, as Russell and early Wittgenstein assumed, then the number of their combinations is large but strictly finite.

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Atomic states of affairs(as the fundamental building blocks of reality in this theory): The simplest, most basic facts about the world that cannot be reduced to anything simpler—like 'this ball is red' rather than complex situations involving multiple parts.
Bertrand Russell: Bertrand Russell was a British philosopher, logician, and social activist (1872-1970) who became famous for trying to show that mathematics could be built from pure logic, and for his clear, witty writing that made complex ideas accessible to everyday readers. He also became a public intellectual who spoke out on major issues like nuclear weapons, religion, and social justice, earning the Nobel Prize in Literature in 1950. Today, he's remembered as one of the most important thinkers of the 20th century who believed philosophy should tackle real-world problems, not just abstract puzzles.
Combinations(as the possible arrangements of atomic states of affairs): Different ways that basic facts can be grouped or mixed together to create more complex situations in the world.
Ludwig Wittgenstein

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