How is Arithmetic different in regards to the definition than the alternative

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Good day all,

My first post 14 hours ago was an inquiry about how I can develop a solid foundation in understanding and applying mathematics to life.

Having got three good responses I've opened up an ages old photo-copied book which I believe will aid me further in my journey.

So I started reading and come to realize I don't understand what Arithmetic means or is.

When I googled for the derivation of it so as to see where the word derives from I ended up finding the definition instead: "the branch of mathematics dealing with the properties and manipulation of numbers."

So I ask, what branches are there in mathematics that deviates from dealing with properties and the manipulation of numbers ?

Is the definition incorrect, am I misunderstanding it ?