linear algebra - How to tell if a set of vectors spans a space . . . Generically you don't know without examing the presumed "basis" vectors You do know that three vectors are sufficient (x,y,z) to span 3-space; any fourth vector must be a linear combination of (x,y,z) There is no more room
combinatorics - Simplify K! (K+1)! - Mathematics Stack Exchange Pretend K=3 That means (K+1)= 4 This means you'd be dividing 3*2*1 by 4*3*2*1 Consider how you'd cancel out multiples by dividing them Like how (2 (5+x)) 2 would just equal 5+x Following that idea we'd pretty much be able to cancel out every number in the numerator, so long as its also in the denominator This would end up canceling every number except for 4 which equals (K+1) Essentially
Why is $1$ not a prime number? - Mathematics Stack Exchange 49 actually 1 was considered a prime number until the beginning of 20th century Unique factorization was a driving force beneath its changing of status, since it's formulation is quickier if 1 is not considered a prime; but I think that group theory was the other force