As an illustration of a mathematical function concept a teacher can write arbitrary numbers, each on a separate, rectangular piece of paper, and then let the students pair them arbitrarily, on the table, and then investigate numerical, mathematical, properties of the those pairs of numbers. The properties may be what sequence the pairs they can be put in, or the order of numbers magnitudes in different pairs.

In the same way we can pair different fruits with, say, CDs (for whatever reason!), we can pair numbers together, and even fruits with numbers! Fruits and numbers are paired when an exchange of fruits for money takes place in an open fruit market! Note how is a third agent present when we pair fruits and numbers. It is the exchange "agent" that motivates pairing and that gives sense to the pairing action.

These examples should reinforce main concept that a function is a pair of numbers and not necessarily a formula that gives y for given x. Function is not always output for a given input. Function is not a formula. Function is a map or pairs of numbers.

[ math, mathematics, mathematical function, function, map ]

In the same way we can pair different fruits with, say, CDs (for whatever reason!), we can pair numbers together, and even fruits with numbers! Fruits and numbers are paired when an exchange of fruits for money takes place in an open fruit market! Note how is a third agent present when we pair fruits and numbers. It is the exchange "agent" that motivates pairing and that gives sense to the pairing action.

These examples should reinforce main concept that a function is a pair of numbers and not necessarily a formula that gives y for given x. Function is not always output for a given input. Function is not a formula. Function is a map or pairs of numbers.

[ math, mathematics, mathematical function, function, map ]

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