Is Norman Wildberger a crank?
Wildberger is a recurring subject on /r/badmathematics including this recent story. He’s almost a crank and has some very very strange views on mathematics. He strongly objects to the use of infinity and proofs and mathematics that involve it, which includes real numbers.
How are real numbers used to solve problems?
Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting. For example, the solution to the equation x2 − 2 = 0 is an algebraic irrational number, indicated by Square root of√2.
Why are all real numbers irrational?
What sets of numbers does belong to? The number is irrational because it can’t be written as a ratio of two integers. Square roots that aren’t perfect squares are always irrational.
Why are real numbers important?
Real numbers are all the numbers on the number line, and there are infinitely many of them. Their types and categories are important because they can give you more information about the problem you are looking at. In fact, certain types of numbers can direct you to further formulas or definitions in mathematics.
What did you learn about real numbers?
The real numbers include integers, rational, and irrational numbers. The number line contains all the real numbers and nothing else. Every real number has a decimal representation. Real numbers can do arithmetic.
What is Wildberger’s theory of natural numbers?
According to Wildberger this is different from the set theoretical definition (from Von Neumann) of a natural number as nested sets, where the level of nesting corresponds the cardinality of the number.
Who is Prof Norman Wildberger?
I am Prof Norman Wildberger and I have been teaching at UNSW in Sydney for 30 years, from which I have recently retired, and before that I taught at the University of Toronto for 3 years and Stanford University for 2 years.
How many videos are there in the Wildberger series?
There are 78 videos in the series, and I’ve only looked at portions of some of them. There’s a lot of well-presented mathematics. The unusual way Wildberger looks at mathematics has some merit to it. Whether he is a crackpot or not is irrelevant.
What is Wildberger’s view on axioms?
Wildberger has at one point stated that he is against axioms put together for merely there utility. In fact he actually considers it a perversion of the original usage of axiom, compared say to Greek mathematics where an axiom was used only when there seemed to be no other simpler concept.