A non-archimedean valuation is a way to measure the size or 'absolute value' of elements in a field, which does not satisfy the archimedean property. This means that there are elements whose size is not comparable with the size of any multiple of smaller elements, leading to a richer structure for analysis. This concept is pivotal in tropical geometry as it enables the exploration of geometrical structures and algebraic varieties through valuations that allow for a better understanding of their properties.
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