MILESTONE 7: Integers

The following lessons provide some basic understanding of Integers.


Mathematics of integers appears to be quite troublesome to most students. But when we look at it as arithmetic with increase and decrease from zero, it becomes easy to grasp.

Confusion takes place because “plus” and “minus,” which represent operations between two numbers, are also used to show a number as “positive” or ‘”negative.” This becomes clear when integers are defined as being referenced from zero.

–1   =    0 – 1

+1   =    0 + 1

This allows us to convert “positive” or ‘”negative” signs into “plus” and “minus” operations, and vice versa.

Furthermore, confusion arises when “plus” and “minus” operate on “positive” and “negative” numbers, giving consecutive signs. However, once we understand that LIKE consecutive signs produce a positive number…

– (–1)      =     +1

+ (+1)      =     +1

…and UNLIKE consecutive signs produce a negative number, the operations are greatly simplified.

– (+1)      =     –1

+ (–1)      =     –1

Here are some videos from Khan Academy on the subject of Integers.

Negative Numbers Introduction

Adding/Subtracting negative numbers

Multiplying and dividing negative numbers


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  • Chris Thompson  On December 14, 2011 at 3:28 PM

    A smooth and easy feeling for + and – is important in philosophy. Without it, one’s thinking bangs up against zero and stops.


  • vinaire  On December 14, 2011 at 4:11 PM

    Understanding of duality is the key to understanding the nature of this universe.

    That requires the understanding of the point from which the dualities needs to be referenced.

    That point cannot be in this universe.



  • Chris Thompson  On December 14, 2011 at 6:25 PM

    wow, I totally missed your point 2nd and 3rd points. Less cryptic please?


  • vinaire  On December 14, 2011 at 7:22 PM

    Zero is the reference point for all other numbers. Zero is in a class of its own. It represents NOTHING, whereas, all other numbers represent something.

    Similarly, the reference point of this universe is in a class of its own. It cannot be a part of this universe. Please see




  • vinaire  On December 14, 2011 at 7:26 PM

    We have, ….. +5 = 0 + 5
    Similarly, ….. +Chair = Brahma + Chair

    Or, …………… +Chair = Unknowable + Chair



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