Robinson's hyperreals evade Berkeley's contradiction only by relocating infinitesimals to a non-standard model, meaning standard mathematics remains committed to no infinitesimal quantities.

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Abraham Robinson(the subject of the statement): A 20th-century mathematician who invented a new way of working with infinitely small numbers (called non-standard analysis), making ideas that philosophers like Leibniz had about infinitesimals mathematically rigorous.
Berkeley's contradiction(the philosophical problem being addressed): A logical problem Berkeley identified: infinitesimals seem necessary for calculus to work, but they're impossible to define rigorously in regular mathematics.
George Berkeley(his contradiction is being discussed in relation to infinitesimals): An Irish philosopher from the 1700s who argued that physical objects don't exist independently of being perceived—basically, things only exist when someone is observing them.
Standard mathematics(contrasted with Robinson's non-standard system): The usual mathematical system taught in schools, based on real numbers and the rules most people learn—the conventional approach.

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