When researching the reflexive, symmetric, transitive, addition, subtraction, multiplication, division, and substitution properties of equality, the sources I found said they were true "for all real numbers". Are any or all of them not true for complex numbers? i.e., is the "for all real numbers" a necessary caveat, or should it say "for all numbers"? Also, I know the reflexive property applies to mathematical objects as well (any mathematical object is congruent to itself). Do the other properties of equality apply to all mathematical objects as well?
2026-03-29 13:40:25.1774791625
properties of equality: real vs. complex numbers
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