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Q: Is 0.9999… repeating really equal to 1?
Mathematician: Usually, in math, there are lots of ways of writing the same thing. For instance: = = = = As it so happens, 0.9999… repeating is just another way of writing one. A slick way to see...
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Q: What are integral transforms and how do they work?
Mathematician: If you have a function f(x) and a function k(x,s) then you can (as long as the product of f(x) times k(x,s) is integrable on the set X) always form another function of a new variable s...
View ArticleQ: Is there an equation that determines whether a question gets answered on...
Mathematician: Yes, but neither the Physicist nor I know it, and its shortest representation in standard mathematical notation is much too long to ever be written down. More precisely, there are an...
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Q: What is Bayes’ rule and how do I use it to improve my life?
Mathematician: Bayes’ theorem in one of the most practically useful equations coming from the field of probability. If you take its implications to heart it will make you better at figuring out the...
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Q: Are beautiful, elegant or simple equations more likely to be true?
Mathematician: It is not uncommon to hear physicists or mathematicians talk about the beauty, simplicity or elegance of equations or theorems, and even claim that they are sometimes led to a correct...
View ArticleQ: How do you answer a question scientifically?
Mathematician: Suppose you’re interested in answering a simple question: how effective is aspirin at relieving headaches? If you want to have conviction in the answer, you’ll need to think surprisingly...
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