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What is a set? Well, simply put, it's a collection.

First we specify a common property among "things" (we define this word later) and then we gather up all the "things" that have this common property.

https://www.mathsisfun.com/sets/sets-introduction.html

​what does property mean in this context?

​I don't get the proper meaning of characteristics and properties in science and maths.

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Sense 2 at https://www.lexico.com/en/definition/property

An attribute, quality, or characteristic of something.

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The properties of "1" are (for example)

  1. an integer
  2. an odd number
  3. a positive number
  4. a number which multiplied by another (second) number, results in a number equal to the second number.

The properties of "2" are not the same as "1". However they share two properties: #1 and #3.