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No one likes having offended another person; hence everyone feels so much better if the other person doesn't show he's been offended. Nobody likes being confronted by a wounded spaniel. Remember that. It is much easier patiently - and tolerantly - to avoid the person you have injured than to approach him as a friend. You need courage for that.
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Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.