In mathematics, Helmut Hasse's local-global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the p-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in the real numbers and in the p-adic numbers for each prime p.
Read more about Hasse Principle: Intuition, Albert–Brauer–Hasse–Noether Theorem, Hasse Principle For Algebraic Groups
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“On principle I dislike an oath which requires a man to swear he has not done wrong. It rejects the Christian principle of forgiveness on terms of repentance. I think it is enough if the man does no wrong hereafter.”
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