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Yes, every Cauchy sequence of real numbers is convergent. In other words, the real numbers contain all real limits and are therefore continuous, and yes the integers are discrete in that the set of integers only contains (very very few, with respect to the set of rationals) rational numbers, i.e. their values can always be accurately displayed unlike the set of reals which is dense with Irrational Numbers. It's so dense with irrationals in fact, that by comparison, the set of rationals can be called a null set, however that is a different topic.

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Q: Is the set of all real numbers continuous and the set of all integers discrete?
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Are integers discrete?

Yes, integers are discrete. Real and rational numbers have a special property that we can find another one of them between any two. This is what makes them NOT discrete. Between any two integers, say 1 and 2, we cannot find another integer. They are discrete.Things we can count are discrete. For example, the number of questions answered during the answerthon is discrete. Temperature is not discrete.


Are integers real numbers?

yesYes, integers are real numbers.


Are some real number integers?

All integers are real numbers, but not all real numbers are integers.


What is the difference between discrete and continuous graphs?

Discrete and Continuous GraphThis will be a very basic definition but understandable one A graph is discrete when one (or both) of the variables has discrete entries, its means that are entered number, without decimal part, so the graph has no continuity, the trace will be broken parts, not a single one.beside a continuous graph is a graph where both variables are continuous, it means that their field's are de Real number, so the trace it's a continuous line.Also we can differentiated because the range are points (in a discrete one) and all the numbers (in a continuous one).


Is it continuous data if you record change for 1 week?

It sounds like the issue here is whether the data is continuous or discrete. If that is the case then the recording period is not of concern. If you are watching a Petri dish and counting the number of colonies on the dish each day then your data would be discrete. If one the other hand you are watching one colony on a Petri dish and measuring its largest dimension each day in centimetres and fractions of centimetres then your data would be continuous. Discrete data is essentially data that comes from the set of integers. Theoretically continuous data comes from the set of real numbers; in practice it comes from the set of rational numbers.


Are all real numbers integers?

No, all integers are real numbers, but not all real numbers are integers. For example, 1.25 is a real number and a non-integer.No.


Is real numbers a subset of Integers?

You have it backwards. Integers are a subset of real numbers.


Are integers real?

yesYes, integers are real numbers.


Which of the following sets of numbers contains multiplicative inverses for all its elements Positive Integers Integers Rational Numbers Real Numbers?

Rational numbers and Real Numbers. The multiplicative inverses of integers are not integers.


What are decimals real numbers natural numbers integers or whole numbers?

Decimals are real numbers. Furthermore, integers and whole numbers are the same thing.


Are all integers real numbers?

Every integers are real numbers.more precisely, integers are the subset of R, the set of real numbers.They are whole numbers with no decimals or fractions


What is a continuous group?

A group has group operations. If these operations are continuous, it is called a continuos group. Addition of the real numbers under addition with the linear topology is one example. If I apply the discrete topology to any group, I can make it continuous. Note: we need continuous function and inverse!