A field is a system of numbers that obeys the addition and multiplication postul

Question

A field is a system of numbers that obeys the addition and multiplication postulates discussed in lecture and given at the beginning of Section 1.3 of the text. The number "1" is called the multiplicative identity because 1 . a = a for every number a. The following Proposition claims that no other number can have this property. Complete the following argument. Proposition. Every field has just one multiplicative identity. Proof. Let F be a field. Suppose that p element F has the property that for all q element F we have p . q = q . It follows that p = 1. Supply the missing step(s) in this argument.

Explanation / Answer

if we are able to get two munbers p and q such that both beong of F

and their multiplication

p.q = q

then this will only be possible if and only if p = 1 {indicative of the multiplicative indenity}

this is true as there is no other number upon whose multiplication with any other number gives the second number as the result.

so p = 1 is true.and its true that is every field there is always present the number 1 (the multiplicative identity)

this sums up the argument

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