On first introduction to the idea of convergence, it is natural to take an optimistic view. However, in certain cases it is clear with moral certainty that whatever else happens, convergence does not.
Consider subharmonics. Proving their bare existence, we begin with a theorem of our own before beginning any proofs.
Suppose a positive constant, some fixed function bounded by a given. From there, find a local maximum. Suppose the velocity of a given around a stationary point, spinning.
Consider any variable whatsoever, and let it be x. It follows immediately that the notation parallel to that for symbol y is denoted by an alternate symbol.
We are always supposing.
We suppose always,
assume the truth.
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Today is the anniversary of the death of celebrated British mathematician, Dame Mary Cartwright (1900-1998), who is considered one of the pioneers of what came to be known as chaos theory. This exercise is a collage of phrases found in this paper she published in 1945.
Too cerebral for a Sunday night :-}