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The author unfortunately has a misunderstanding of equality. Quoting him, "The equal sign is another mathematical concept that’s often misunderstood. It means,
by scscsc 7y ago
The author unfortunately has a misunderstanding of equality.
Quoting him, "The equal sign is another mathematical concept that’s often misunderstood. It means, of course, that whatever is on either side of the equal sign is equivalent." This is actually wrong.
The equals sign (=) is a shorthand for stating not that the two sides are equivalent, but that they are the same (i.e., they are equal).
If they were just equivalent, we would use another sign, like ≡ (unicode U+2261).
- adriand 7y ago(2 + 3) and 5 are not “the same”. If we’re using ordinary English language to discuss this issue I think “equivalent” is a sensible choice.
- scscsc 7y agoAs expressions, sure, they are not the same. But "2 + 3 = 5" is a statement about numbers, not about expressions. When you talk about numbers (the object of study), you do not (usually) talk about arithmetic expressions. Arithmetic expressions are part of the language used to talk about numbers. When talking about arithmetic expressions themselves, you would use a meta-language (e.g., English). The arithmetic expressions would then be called the object-language (the language being studied). All of this should be pretty clear after taking a serious course in Logic. I am not saying the choice of words is not sensible, I'm saying it it factually wrong.
- deleted 7y ago[deleted]