鰹

 I write a diary in English to study English.

According to my text of linear algebra, "a straight line" is defined as follows.

 E is a vector space. K is the coefficient field. x belongs to E and  is not a zero vector. And x is one element of E. "A straight line" is defined such that : { λx ; λ ∊ K }.

  I suppose that "one element of E" is a vector that cannot be represented by  sum of vectors that are not scalar multiple of the vector. If not, the replacement theorem following to the definition does not make sense, I think. 
  However, the existence of "one element" is not  obvious. So I tried to prove it using reductio ad absurdum.  But failed.

  This is the end of my day.