Mathematics

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In mathematics numbers are abstract notions. But when we divide number say we do 1 divided by 2 i.e. ½ does this mean abstract notions are divisible. It gives me a feeling like abstract notions have magnitude but then it comes to my mind that abstract has no magnitude.1=1/2 + 1/2 can we say the abstract notion 1 is equal to the sum of two equal half abstract notions? How should I conceptualize the division? The other part related to abstract notion is that how is the abstract notion of number 1 different from the unit cm? how can we say that the unit cm is abstract when we consider it a definite length. How is the unit apple different from unit cm if I count apples and measure length respectively? I am in a fix kindly help me to sort out this. I will be highly- highly grateful to you.
Accepted:June 7, 2013

Accepted:

June 7, 2013