Thread: A better explaination of domain is discrete or continuous?

1. A better explaination of domain is discrete or continuous?

I'm not exactly sure what these two are so can someone explain it? And are any of the below wrong?

1. The number of hits on your web page.
The domain is discrete.

2. The temperature of a cup of hot chocolate.
The domain is continuous.

3. The amount of calories in your food.
The domain is discrete.

4. The weight of a baby.
The domain is discrete.

2. Re: A better explaination of domain is discrete or continuous?

What would you think if someone told you that they had 15,238.119 hits on their webpage?

What would you think if someone told you that they owned 2.119 cars?

Is it possible that you have 3.6455 brothers?

COMPARE

Could the distance to City Hall from here be 3.6455 km?

Could the thermometer read 30.198 degrees Celcius?

Could the average person in some city have 3.6455 brothers?

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The problems #3 and #4 are poor questions. Calories and weights are always REPORTED discretely, but are in fact measurements and so in fact come in a continuum. Someone could understand this concept perfectly, and still choose the "wrong" answer here. Those are bad problems!

3. Re: A better explaination of domain is discrete or continuous?

So discrete can means that it can be in parts (fractions, decimals) and logical while continuous means it has to be a whole in order to be logical? :S

4. Re: A better explaination of domain is discrete or continuous?

Discrete = counting numbers - fractions/decimals make no sense
Continuous = real numbers - "no gaps" - what measurements in the real world give you (time, distance, weight, energy, etc) - fractions/decimals make sense

Some cases are kinda tricky. Money comes in fractions, but is discrete, because the fractions can only go down so far. In US currency, if we measured everything in cents rather than dollars, then there would be no decimals. But even that isn;t true. Gasoline price come in factions of a penny, and so can some financial valuings. However, money is still discrete, because unlike, say, temperature, you simply don't have a continuum there even with these special cases. There are gaps. \$19.997352735975924 simply doesn't make sense. COntinuous means that, in theory, you could keep measuring it as finely as you liked. Something weighing 19.997352735975924 kg makes sense, even though our instruments are nowhere close to being that accurate.