14-240/Tutorial-Sep30: Difference between revisions

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* <math>S</math> satisfies all the properties of the field except distributivity.
* <math>S</math> satisfies all the properties of the field except distributivity.


* <math>\exists x \in S, 0x\neq 0</math>.
* <math>\exists x \in S, 0x \neq 0</math>.


Solution:
Solution:

Let <math>a \in S</math> be the additive identity and <math>b \in S</math> be the multiplicative identity where <math>a \neq b</math>.


==Nikita==
==Nikita==

Revision as of 20:35, 4 October 2014

Boris

Problem

Find a set of two elements that satisfies the following:

  • satisfies all the properties of the field except distributivity.
  • .

Solution:

Let be the additive identity and be the multiplicative identity where .

Nikita