Mathematical objects

What are numbers, sets, groups, points, etc.? Are they real objects or are they simply relationships that necessarily exist in all structures? Although many disparate views exist regarding what a mathematical object is, the discussion may be roughly partitioned into two opposing schools of thought: platonism, which asserts that mathematical objects are real, and formalism, which asserts that mathematical objects are merely formal constructions. This dispute may be better understood when considering specific examples, such as the "continuum hypothesis". The continuum hypothesis has been proven…

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Source: List of philosophical problems (CC BY-SA 4.0)