Numbers can be understood from the following two aspects.
1, different from the previous definition of logarithm, number can be used to represent not only quantity, but also quality, process and all material phenomena in nature.
2. Numbers are graphic symbols and one of the representations of quantity. There are countless representations of quantity.
3. Generally, people use the number "1" to represent the quantity specified in the standard unit, and other numbers are generated on the basis of "1".
Philosophical significance of the definitions of number and quantity
1 reveals the essence of quantity and defines quantity more comprehensively and accurately. The original definition of quantity is to illustrate what quantity is with examples, but it does not reveal the essence of quantity and cannot fully reflect the object described by quantity.
2. Solve the circulation problem of quantity and number in the definition.
3. All phenomena that matter shows to the outside world are attributes, which can be expressed by quantity. So Pythagoras, an ancient Greek philosopher, would say that "everything counts".
4. Make the relationship between quantity and quality clearer. Quantitative change means that the attributes of things have changed, and attributes are divided into essential attributes and non-essential attributes. For essential attributes, quantitative change is qualitative change, and tiny quantitative change is tiny qualitative change. As for when people's weighing becomes "qualitative change", it depends on the actual situation. For example, some quantitative changes are continuous, even and uninterrupted, such as age and height. Young people become middle-aged people, and middle-aged people become old people. These should all be qualitative changes, but there is no clear boundary from middle age to old age. This is completely artificial. This is also the reason why knowledge is vague.
5. Quantity depicts the difference of the same attribute, so quantity is the deepening of people's understanding of things' attributes and the accurate understanding of things' attributes. Therefore, Marx said that "a science can only be truly perfect if it successfully uses mathematics".
6. According to the definitions of quantity and number, the concept of mathematics can be redefined to make its connotation more accurate, thus making the relationship between mathematics and other sciences clear at a glance.