2
$\begingroup$

The additive identity is 0.

The multiplicative and exponential identities are 1.

Exponentiation is repeated multiplication, and multiplication is repeated addition.

If you go up a further level, to repeated exponentiation, the identity is again 1.

If you use Knuth's Up-Arrow Notation, and the principles behind it, it's simple to see that 1 is an identity for all higher operations.

Why is addition the only operation with a different identity?

$\endgroup$
3
  • $\begingroup$ Let a,e be in R where e fulfills a+e=a for all a, then e must be 0... But you probably know that. $\endgroup$
    – 355durch113
    Commented May 20, 2014 at 19:38
  • 2
    $\begingroup$ Exponentiation (and higher operations) has no two-sided identity. $\endgroup$
    – Daniel Fischer
    Commented May 20, 2014 at 20:24
  • 1
    $\begingroup$ There is no exponential identity. You shouldn't think of exponentiation as the sort of thing that has an identity; in particular, it's not associative. $\endgroup$
    – Qiaochu Yuan
    Commented May 20, 2014 at 20:25

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .