This post may be repetitive but I had an interesting conversation with a former teacher and wanted to get the information down again. The absolute value of plus 2 might be considered to be plus 2 again or unsigned two. The school system may mix these two concepts and confuse children.
In one approach, plus two is a primitive object. As is minus 3. Signed numbers are consider not to have structure but to be objects that are not split in one approach.
In another approach, signed numbers are a composite object. They are a pair of a sign and a size. Or a sign and a magnitude. Sizes or magnitudes are considered primitive concepts. In this approach, words have to be used to indicate that magnitudes or sizes are first class concepts and are being used. Words can include size, magnitude or unsigned number. In this approach, the absolute value of a signed number is the associated size or magnitude. The absolute value of plus two is then unsigned two or two magnitude or two size. The extra word can be used to indicate it is a size or magnitude not a signed number.
Historically, humans developed the concept of unsigned number first. Then signed numbers were added. In doing so, they used words for unsigned numbers to apply to signed numbers. This creates confusion. For example 2 is greater than -3 is often confusing. Two is more positive than -3 is not confusing. If needed, greater in sign or greater in size can be used as a phrase to indicate which usage is intended.
