Equality (mathematics) Facts for Kids

In mathematics, when two things are equal, it means they are exactly the same in every way. They have the same value and the same properties. Mathematicians use the equals sign (=) to show this. So, if you see "x = y", it means x and y are the same.

Sometimes, things aren't exactly the same but are still 'equivalent' in a special way. This is called an equivalence relation. It means they are related in a specific way. We often use symbols like $\sim$ or $\equiv$ to show this kind of equivalence.

When we say two expressions have the same value, we write an equation. For example, 2 + 3 = 5 is an equation. If things are not equal, we call it an inequality.

Equality is also a transitive relation. This means if one thing is equal to a second thing, and that second thing is equal to a third thing, then the first thing is also equal to the third thing. For example, if A = B and B = C, then A must also be equal to C.

In math, if something is true about one variable, it must also be true about the other variable for them to be considered equal. If even one thing is different, they are not truly equal in a mathematical sense.

Equality in Geometry
- Congruent Shapes
- Similar Shapes
Equality in Computer Science
- Pointers and References
- Comparing Values
Equality in Social Sciences
Related pages
See also

Equality in Geometry

In geometry, we often use the word congruence instead of equality. Numbers are equal, but geometric shapes are congruent.

Congruent Shapes

Two shapes are congruent if you can move or rotate one of them so that it fits perfectly on top of the other. They are exactly the same size and shape.

Similar Shapes

If you need to shrink or enlarge one shape to make it fit the other, then they are not congruent. Instead, they are called similar. Similar shapes have the same shape but different sizes. The symbol for congruence is $\cong$ , while the symbol for similarity is $\sim$ .

Equality in Computer Science

In computer science, the idea of equality is usually the same as in mathematics. When comparing if two things are equal, programmers often write == (two equals signs). The single equals sign = is usually used to give a value to something, like `x = 5`.

Pointers and References

In some programming languages, especially object-oriented ones, things can get a bit tricky. These languages use 'references' or 'pointers'. A reference is like an address that points to where a piece of information is stored in the computer's memory.

If two references point to different places in memory, even if the information at those places looks the same, the references themselves are considered different. So, `a == b` might be false if `a` and `b` point to different memory locations, even if the data stored there is identical.

Comparing Values

Because of this, many programming languages have another way to compare things. For example, in Java, there's a special method called `equals()`. This method compares the actual values of the objects, not just where the variables point. So, `object1.equals(object2)` would check if the content of `object1` is the same as the content of `object2`.

Equality in Social Sciences

In social sciences, the idea of equality is about how people are similar or have the same opportunities. Two people might be seen as equal if they have similar levels of education, money, or age.

Another word for a person who is equal to another person in terms of status or ability is a peer. For example, students in the same grade are often considered peers.

Equality (mathematics) facts for kids

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