object of mathematics

object of mathematics 

study numbers and the various correlations between them, independently of the concrete nature of the magnitudes and laws which lead us to these numbers and correlations. One of the fundamental concepts is that of magnitude and its measurement.

 It is characteristic of a magnitude that it can be measured, i.e. it can be compared in one way or another with some specific magnitude of the sort which is accepted as the unit of measurement.

every magnitude is related by its measurement to an abstract number. This number depends essentially, however, on the unit assumed for the measurement, or on the scale.

On increasing this unit, the number measuring a given magnitude decreases, and conversely,

the number increases on decreasing the unit.

The choice of scale is governed by the character of the magnitude concerned and by the circumstances in which the measurements are carried out. The size of the scale used for measuring one and the same magnitude can vary within the widest possible limits — for instance, in measuring length in accurate optical studies, the accepted unit of length is an Angstrom (one ten-millionth of a millimeter, 10^10m); whereas use is made in astronomy of a unit of length called a light year. the distance travelled by light in the course of a year (light travels approximately 300,000 km in one second).

the source:
A COURSE OF Higher Mathematics VOLUME I. SMIRNOV.
By: Fady tarek