why axiom 5 in the list of Euclid's axioms, considered a 'universal'?
Answers
""" ❤️ Answer ❤️ """
Axiom 5 of Euclid's Axioms states that - “The whole is greater than the part.”
This axiom is known as a universal truth because it holds true in any field of mathematics and in other disciplinarians of science as well.
Let us consider a line segment AB. Mark two points P and Q on
AB is a whole part.
It is divided into three parts: AP, PQ, QB.
AB = AP + PQ + QB
Thus, we see that
AB > AP
AB > PQ
AB > QB
Hence, AB (whole) is greater than its parts i.e, AP, PQ, and QB.
Let's take some practical facts to understand this.
Bangalore is a part of Karnataka which means that Karnataka is larger than Bangalore. i.e. Karnataka > Bangalore.
India is a part of the world which concludes the world is larger than India. Here the world is a whole whereas, India is just a part of it.
Therefore, it is true that the whole is greater than the part that is considered as universal truth.