The Poorna Mantra

Have you ever been confused with the indeterminate forms ( 0 / 0, ∞ - ∞ ) in Mathematics? Have you ever failed to understand the intricacies of Discrete Mathematics? Have you ever faced issues with Set Theory or Equilibriums in Physics? Keep your worries aside and read this philosophical point of view provided by the Sanskrit Poorna Mantra. It will definitely give you a different perspective of looking at these mathematical terms.

(Om poornam-adah poornam-idam poornat-purnam-udachyate

poornasya poornam-adaya poornam-eva-avashishyate) 

Let us go by its word by word translation first:

पूर्णमदः (poornam-adah) means ‘that is complete’. पूर्णमिदं (poornam-idam) means ‘this is complete’. पूर्णात्पुर्णमुदच्यते (poornat-purnam-udachyate) means ‘from completeness comes completeness’.

पूर्णस्य पूर्णमादाय (poornasya poornam-adaya) meaning ‘if you remove completeness from completeness’ पूर्णमेवावशिष्यते (poornam-eva-avashishyate) meaning ‘completeness is what remains’.

This is a poetic construction made on the word पूर्ण (Complete), and there is much deeper meaning to it than what appears on the face of it. If you actually think about it, it explains some interesting concepts in Mathematics and Science.

So, let's delve deeper into its real meaning:
पूर्णमदः (poornam-adah) means the outer world or the material world is complete. That is, the world as can be experienced by our five senses is complete. पूर्णमिदं (poornam-idam) uses the word "idam" meaning "this". We use the pronoun "this" to indicate things closer to us. What can be closer to us than the things that we experience with our senses? It is what we experience with out mind! The inner world, the spiritual world! It means that the Spiritual world as experienced by human mind is also complete. 

Furthermore, the two "complete" things are not mutually exclusive sets. From completeness comes completeness. It tells us that from the vastness of the material world, the complete nature of the outer world, comes the vastness or completeness of your mind. Conversely, a complete mind completes your material world. This is what is double implication ( Inner Completeness ↔ Outer Completeness ). The two complete worlds enrich each other and that is how a human being matures throughout the life. Education helps you enhance your understanding of the outer world while spiritual development helps you understand yourself. They both together make the human life "complete". 

So, there you have your first set of equations using ∞ (completeness). Consider natural numbers ( 1 to ∞ ) as the indicators of completeness with infinity being the most complete ( The catch here is that you don't know what is "the most complete", just like you don't know what is the highest number. It is ∞ )

(natural number) + ∞ = ∞
∞ + (natural number) = ∞
(natural number) * ∞ = ∞
∞ * (natural number = ∞  
∞ + ∞ = ∞
∞ * ∞ = ∞

This shows that if you find complete understading of even one of the worlds, it can be enough to get you closer to overall understanding of the life.

The second part is even more beautiful because if tells you the importance of finding total completeness, total control and understanding of both the realms and this is where the essence of this mantra lies. It says that if you take out completeness from completeness, you will find only completeness. That is, once you reach the state of utmost completeness and achieve control over your senses as well as your mind, you will never lose that control. You will reach a state of stable equilibrium!

∞ - (anything) = ∞ 

Reading between the lines:
If you are a zero or worse in any of the things, then you are doomed!
  
0 * ∞ = indeterminate
∞ * 0 = indeterminate
∞ - ∞ = ∞ + (-∞) = indeterminate