What Is The Difference Between Inverse VS Reverse VS Converse
Sometimes it can be hard to know the difference between inverse, reverse, and converse. The terms are often used interchangeably when they all have precise meanings.
Inverse, reverse, and converse are all types of opposites, and knowing their differences will help you better understand how these things work.
Let’s get started by defining each term so you can recognize when you see them being used correctly.
The composition of two inverses is again an inverse. The composition of two adjoints is again an adjoint; thus, every linear operator on a finite-dimensional vector space over a field has an adjoint.
However, not every linear operator on a finite-dimensional vector space over a field has an inverse: there exist examples of unbounded operators with no inverse because they are not one-to-one.
A bijective function whose inverse is also bijective is called a homeomorphism or topological or continuous isotopy.
A continuous bijection with a compact domain and codomain is called an open map or closed map if its range equals its codomain.
An open map whose range equals its codomain is sometimes called topologically trivial. Still, that term does not imply that it is injective and open.
A topological mapping from X onto Y between topological spaces induces a homeomorphism from Y onto X if it induces both inclusions.
Inverse Operator: The inverse operator changes a positive statement into its negative form by negating all variables.
Consider a simple mathematical equation y = 2x + 3, where x denotes some variable whose value will change according to different situations.
Reverse: Linguistic Meaning and Math Equivalence
In mathematics, a reversed function looks at all its inputs and outputs them in reverse order.
For example, if you take a list of numbers from 1-100 and put those same numbers into a function with an input like input_list(20), it would produce an output like 20,19,18…1.
If it were reversed (input_list(1)), it would give you 1,2,3…100. Reverse means to turn around or put something back to where it was. And as far as math functions go, there are many reversible ones; most of these are addition and multiplication functions.
The only operations that aren’t reversible are division and subtraction. This makes sense because the division is essentially subtraction on steroids. It takes one number and divides it by another number.
Converse: Logic, Definitions
The term converse can be used for logic, definitions, and proofs. Adwords converse refers to a statement’s opposite.
For example, if you say that all squares are rectangles, you have just made a statement called the converse of all rectangles are square,” or simply the converse of all squares are rectangles.
This means that if something is not a square, it can’t be a rectangle it must instead be an object which isn’t either.
Conversely (pun intended), if something can’t be square and rectangle (like triangles or trapezoids), it must only be one of those things at any given time and place.
In other words, if something can’t be a square, it must be a rectangle and vice versa. Logically speaking, there is no middle ground: you’re either one thing or its opposite.
In addition to being used in logical statements like these, the converse also applies when talking about definitions and proofs: If we know what a word means based on its definition or after proving it with formal logic, we know what its converse is as well. So, now take a look at the difference between them.
Difference between inverse vs. reverse
Inverse and reverse variations are somewhat similar ideas, but each has different applications.
Inverse variation implies that as one factor becomes more common or more significant, another factor will become less common or more minor.
Reverse variation means that as one factor becomes more common or more significant, another factor will become less common or more minor in an opposite way.
The converse is most often used to describe a relationship of words and phrases in which a particular word can be used to replace another particular word.
For example, in and out are converse words because you can use either to say whether something is inside or outside.
When it comes to relationships between variables, though, there’s no inverse variation; instead, it’s called negative correlation.
For example: As temperature increases, pressure decreases; as pressure decreases, temperature increases. These two variables are negatively correlated because when one goes up (or down), so does its opposite number on the other side of zero.
Difference between inverse vs. converse
In mathematics, inverse and converse refer to two different ways of relating statements. An inverse statement implies that if one thing is true, another is false.
The first term in an inverse statement refers to a necessary condition for some result. In contrast, the second term refers to a sufficient condition for some result.
Inverting (or switching places) with terms produces a converse statement. A converse statement implies that if one thing is true, another is also true.
For example: If it rains today, I will bring my umbrella. This can be expressed as inverse: It will rain if I don’t bring my umbrella today. A converse statement has precisely the opposite meaning from its original statement.
Inverse, reverse, and the contrapositive are three basic logical operators. Logical operators can be used to conclude several premises, thus deriving what is known as an inference.
In everyday language, these operators can be defined as an idea that reverses another idea or the reversal of an idea. For example, if you say I hate carrots, you have come up with an idea (the opposite) of liking carrots.
This, in turn, means that you have also said something about hating potatoes since they are a vegetable too. If you think about it logically, it becomes clear that if you do not like one vegetable, you cannot like any other vegetable.
Hence comes the concept of the inverse operator in logic which means reversing an idea to derive its opposite or vice versa. The same goes for the reverse and contrapositive operators, which means going against an idea to get its opposite or going against an idea to get its original statement. The only difference between them is their use case scenarios.