About Two Envelope Paradox

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The first time I came across a term recreational mathematics ┬áI didn`t quite catch what it was referring to. Math never seemed to me like an activity that would be undertaken solely for entertainment purposes, although I have experienced a certain level of serenity while solving a batch of math problems in the past, particularly if they were adequate to my knowledge. Methodical completion of individual problems fires periodic dopamine doses in my brain resulting in an overall feeling of satisfaction. Recreational mathematics refers to a set of math problems that have no obvious practical or theoretical applications if solved, and functions more like brain teasers for mathematicians and philosophers to tackle with their skill set. Although existing solely for entertainment purposes, these seemingly useless problems can sometimes reveal some fundamental characteristics of mathematical world, like a question whether mathematics could be established using only formal logic. This problem was indeed pursued by mathematicians at the beginning of the 20th century – without definitive results. To my knowledge, no one managed to cram mathematics into the boundaries of formal logic, although different opinions exist on this topic. The quest for logicism, although ambitious, was ultimately unsuccessful. One simple recreational mathematics problem, although not directly an argument against logical axiomatic mathematical system, illustrates the dichotomy between mathematics and common sense. It is called The Two Envelope Paradox. Although there are numerous different explanations to this paradox and ways to solve it, I am going to explain the basic premise of it and give you some of my own observations.

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