The Transitivity of Equality

-Nihilist Numbat

Frantum sat upon the stool pondering over the hot sunny weather. It was a rather sticky afternoon. He could hear the murmur of students whispering among themselves. The lecture was about to begin. Being a professor of Mathematics, she knew how reluctant the children were about studying anything at all.

“Equality,” she said starting in the middle of the next lecture, “is a binary operator”. The students peered at him quizzically. She had a chalkstick in his hand and held an umbrella in another. Waving her arms, she jotted down some symbols on the blackboard. After writing a few equalities, she turned around. Going on, she said, “Unlike the other binary operators like the inequality, the transitivity of equality is not a law. Simply put, this means that if A equals B and if B equals C, it might not necessarily mean that A equals C.”

Cold wind of the night breezed over them. Birds chirped in the vicinity. The park had delightful greenery that lit up in the afternoon sun. The chirps of a cricket could be heard, as the bowler hit a six while getting caught out by the batsmen.

Frantim continued to bore the students with more concepts of abstract binary operators. The park was a rather dull one.

“Since inequality is not a relation but a binary operator, there is no question of it being an equivalence relation. But unlike other relations, equality is definitely a relation. And hence we can try to justify it being an equivalence relation.”

Irritated at this, one of the students raised his hand. The professor looked at him while holding a rope in his hand. The rope will have no further relevance in the story.

“Professor,” said the bearded student silently, “I can understand why the transitivity of equality is not a definite property among all the objects in the universe. But wouldn’t that lead to wilful number of contradictions?”

The professor stared back at the student with a frog in his mouth. The waterfall behind him simmered in utmost glory. “Well maybe,” he started saying after a little thought, “Maybe the contradictions are all around us but we don’t notice them. Mathematics does not need to have contradictions. It just needs to have a professor who can speak. When I was asked to teach you guys some mathematics, I wasn’t even asked. And neither did any of you volunteer. But look at us! Aren’t we all in a classroom?”

The students seemed to agree. The graveyard had quite a calm and soothing atmosphere to enjoy a circus. The cricket match had ended and everyone holding the ball danced holding each other’s arms. Evening had sat on the last bench of the lecture hall. One of the students screamed in agony and vanished, shocked at listening to the bark of the car parked nearby.

The class ended. Franctem continued to shave his head with the rope.

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