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Indranil
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If the dimension of A and B are different, then how to express the dimension of A and B together? how to write?
Could you explain why multiplications are ok but additions are not? It could be division like A/B or could be A-B. I am confused. Please get it clear.fresh_42 said:Simple rule: multiplications are o.k., additions are not. Can you give an example what you mean, and especially what "together" means?
If you add a measured number of pounds (force) to a measured number of miles, you get garbage. If you change one unit or the other, the result will change. But by no fixed proportion.Indranil said:Could you explain why multiplications are ok but additions are not? It could be division like A/B or could be A-B. I am confused. Please get it clear.
##A/B = A \cdot B^{-1}## and ##A-B= A + (-B)##, so from a mathematical point of view, there is no difference between multiplication and division, resp. addition and subtraction. Addition is obviously not allowed, because there is no common domain where it would make sense to add, e.g. length to time. By multiplication we define a new domain of the multiplied dimension, e.g. distance per time results in velocity which is a new dimension. One could probably formally construct domains with length plus time, but this has no useful real life correspondence. It will always remain a pair (length ; time) whereas length / time consists of all possible velocities.Indranil said:Could you explain why multiplications are ok but additions are not? It could be division like A/B or could be A-B. I am confused. Please get it clear.
The difference in dimensions between A and B can be expressed using various mathematical symbols, such as the minus sign (-) or the division symbol (/). For example, if A has dimensions of 10 units and B has dimensions of 5 units, the difference in dimensions can be expressed as A - B = 5 units or A / B = 2.
Yes, for instance, if A has dimensions of length, width, and height (LWH) of 5cm, 3cm, and 2cm respectively, and B has dimensions of LWH of 8cm, 6cm, and 4cm respectively, the difference in dimensions can be expressed as A - B = 3cm, 3cm, 2cm or A / B = 5/8, 3/6, 2/4.
The unit used to express dimensions will depend on the type of dimensions being compared. For example, if A and B have dimensions of length, the unit used could be centimeters, meters, or inches. If A and B have dimensions of volume, the unit used could be cubic centimeters or cubic meters.
One way to express the difference in dimensions visually is by using a diagram or graph. For instance, a bar graph can be used to show the difference in dimensions between A and B, with the length of the bars representing the dimensions for each object.
Yes, the difference in dimensions can also be expressed using words or phrases. For example, the dimensions of A can be described as larger or smaller than the dimensions of B. This method may be more useful when explaining the difference in dimensions to someone who is not familiar with mathematical symbols.