‘The most famous was his diagonal argument which seems to show that there must be orders of infinity, and specifically that the non-denumerably infinite is distinct from the denumerably infinite.’

‘This amounts to saying the transfinite whole is not equal to the sum of its denumerably infinite parts.’

‘This way of reasoning is also present in finite and denumerably infinite collections.’

‘Imagine the hotel filled to capacity with denumerably many guests.’

‘This type of space requires a slightly different treatment to spaces of finite, or denumerably infinite, dimensions.’

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