What is Discrete Math (in layman's terms)?

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wlcgeek
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Wikipedia says it deals with distinct objects and is differentiated from continuous math, which has objects that "vary smoothly."

For a layman, can someone explain what this means?

And is all math discrete or continuous? No other options?
 
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Discrete mathematics deals with values or concepts which have countable results. Key word being countable (meaning discrete).

Calculus is a mathematics which deals with continuous ideas such as limits and infinity.