Subtractions 

Removing Objects from Sets

Subtraction is nothing but removing objects from existing mass sets.

For example, suppose we have 26 mangoes and someone wants 25 mangoes.

Step‑by‑Step Removal

Units place (rightmost):  

• 6 mangoes – 5 mangoes = 1 mango left.

Tens place (next set):  

• 20 mangoes – 20 mangoes = 0 mangoes.

• Result: Only 1 mango remains.

 Borrowing Rule

Now suppose we subtract 17 mangoes from 26 mangoes.

Start with the units place:

• 6 – 7 is not possible, because 7 is larger than 6.

• So we borrow one full set (10 mangoes) from the tens place.

  • The 6 becomes 16.

  • Subtract: 16 – 7 = 9 mangoes.

• The tens place loses one set:

  • 20 – 10 = 10 mangoes.

  • Then 10 – 10 = 0 mangoes.

• Result: Only 9 mangoes remain.

 Why Borrowing Works

• Borrowing does not create new objects.

• It simply relocates one full set from the left digit into the right digit.

• This ensures subtraction always conserves mass: nothing disappears, only shifts between sets.

Negative Numbers — Part 1: Subtractions

 No Mirror Line Before Zero

In the Ardhanārīśvara Number Line, there is no negative mirror line before zero.

• Zero itself is not a separate number on the line.

• Abstract numberlilne ..........-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.......

• Every number is written with 0 first, then the number: 01, 02, 03, 04, 05.....…

• Here, 0 means space (absence of property), while the number after it represents mass occupying that space.

 Measuring Mass in Space

When we measure volume, distance, or weight, the 0 (space) is replaced by the property being measured, and multiplied by the number of units.

Example:

• A ball has 5 cm³ volume.

• 4 balls → 5 cm3×4=20 cm3.

• Space (0) is the background, mass (1,2,3…) is the measurable presence.

 Subtraction as Shortage

Suppose I have 4 mangoes, but someone asks for 5 mangoes.

1. Write the larger number first (the demand): 5.

2. Subtract the available stock: 5 – 4 = 1.

3. Since the demand was larger than supply, we must add a negative sign.

Result: –1 mango.

But this does not mean an “opposite mango.”

• It is not anti‑matter.

• It is simply an unfulfilled promise or underperformance marker.

 Visual Ledger Example

• Seller’s line: 🥭🥭🥭🥭 + shortage obligation (–🥭).

• Buyer’s line: demand of 5 mangoes.

• Transaction shows –1 until the seller fulfills the shortage.

• Once fulfilled, the negative collapses into 0, and the buyer’s line begins with +5 mangoes.

 The Material Axiom

Negative numbers in the Saraswati Number System are not opposites of positive numbers. They are shortage markers, recording obligations until fulfillment. Zero is reconciliation, not emptiness, and every number is written as 0 + mass presence (01, 02, 03…).