Some basic terminology This question is related to a topic in Physics but i think that it is more of a Mathematical question.
BACKGROUND
I am trying to study Physics rigorously from the beginning.  I am trying to understand each and every word (of course along with the idea). The first topic that i have to study is Measurement. It involves words and phrases like "quantity" and "physical quantity" and i do not think i know what they really mean. After some critical thinking about these terms, i realised that i should know the meanings of four more terms: object, property, mathematical object and number. After analysing these all i ranked them according to the order in which i should study about each. Here are the ranks:
1 .Object
2 .Property
3 .Mathematical object
4 .Number
5 .Quantity
6 .Physical quantity

I looked up the terms in the dictionary, the internet and also thought about them and analysed them myself. This is my interpretation of them along with which part of speech they belong to:
1 .Object :(noun) An object is an entity which can be perceived by our senses. It has an identity, characteristics (properties or attributes) and behaviour. 
Objects can be classified into two types:
(I)Abstract objects : Abstract objects are those objects which do not have physical existence.
(II)Concrete objects : Concrete objects are those objects which have physical existence.

2 .Property :(noun) Property is an abstraction of behaviour of an object. An object may have many properties.
Concrete objects basically have two types of property:
(I) Physical property : A physical property of an object is a property that can be observed without changing the composition of matter. Example : appearance, texture, color, odor, melting point, boiling point, density, solubility, polarity, and many others, etc.
(II) Chemical property : A chemical property of an object is a property that can be observed during a chemical reaction and thus changing the objects composition (chemical composition). Example : heat of combustion, reactivity with other chemicals, flammability, and types of bonds, etc.

3 .Mathematical object :(noun) A Mathematical object is an object arising in Mathematics. In mathematical practice, an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs. e.g. :number, matrix, etc.

4 .Number :(noun) Number is a Mathematical object used to count, label and measure. There are many types of numbers - Natural numbers, Whole number, Real numbers, etc.. It is an idea. To represent numbers we use numerals and to write numerals we need digits.

5 .Quantity :(noun) The extent, size, or sum of countable or measurable discrete events, objects, or phenomenon, expressed as a numerical value.

6 .Physical quantity :(noun) A physical quantity is a quantity in used in physics to express the "size" of a physical property of an object.

MY QUESTIONS
Am i good to proceed? 
How correct am i in describing the above terminologies accurately and rigorously?
Is there anything that is needed to added to make them more accurate and concise? 
 A: I'm not entirely sure this does belong on this site, since in essence you're asking:
"What basic terminology and definitions are the most fundamental starting point for a rigorous study of Physics?"
You've assumed that the answer includes many mathematical terms, which is why you've placed the question on this site.  However, I disagree with that assumption.  I'll answer your question in any case, in the above paraphrased form.
The most basic terms to learn to fully understand Physics* are as follows:


*

*Physics

*matter

*energy

*space

*time

*science

*observation

*scientific method

*hypothesis

*theory

*experiment

*object

*property

*measure


From there you can descend to the various properties of objects and how to measure them, and the theories which allow accurate prediction of the measured results of experiments.

It's true that understanding these terms may involve understanding other terms first—but that doesn't mean that the other terms are even physics terms, or that they belong in a list of key words for the subject of Physics.  The word "number" is an example; you likely can't fully clear "measure" without some understanding of "number," but "measure" is a key word for Physics and "number" is not.

*I won't say "rigorously" since you didn't define that term and the usual meaning applies specifically to mathematical proofs.
