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Induction 13
TheMathsters
553 views
Proof by induction that if alpha + 1/alpha is an integer, then alpha^n + 1/alpha^n is an integer, for all natural numbers n.
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Functions 5
TheMathsters
1,474 views
More examples with more formal proofs of injectivity and surjectivity, and proofs that functions are not injective and surjective
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Functions 4
TheMathsters
1,125 views
Looking at some examples of functions to see if they are injective and surjective, introducing bijective functions at the end
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Functions 3
TheMathsters
1,051 views
Introduction of injective and surjective functions, with definition at the end
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Functions 2
TheMathsters
806 views
Some more examples of functions, definition of composition, proof that composition is associative.
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Functions 1
TheMathsters
1,083 views
Definition of function and a few examples
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Numbers 16
TheMathsters
462 views
Using Euclid's algorithm backwards to show that if hcf(x,y)=h, not necessarily 1, we can get an expression rx+sy=h
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Numbers 15
TheMathsters
396 views
Another example of Euclid's algorithm backwards to show that if hcf(x,y)=1 we can get an expression rx+sy=1
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Numbers 14
TheMathsters
512 views
Using Euclid's algorithm backwards to show that if hcf(x,y)=1 we can get an expression rx+sy=1
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Numbers 13
TheMathsters
436 views
Proof of the converse to the result in Numbers 13: that if "p|ab implies p|a or p|b" then p must be prime.
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