Equal vs Equivalent
Equal and equivalent are terms or words that confuse many not having a math background. This is because those having studied sets in math know that equivalent does not mean identical or the same. There are similarities between things or objects that are equivalent. However, it would be wrong to Say that equivalent things are equal as there are differences between the two.
Equal
When two things are same or identical in amount or quantity, we call them as equal. For example, students obtaining same number of marks are treated equals while two circles having the same area are also considered equal circles. If two people make use of the same dumbbell sets and raise it the same number of times, they are said to have completed equal number of sets. In math, two sets are said to be equal if they contain the same number of elements and also the same elements though the order of elements in the two sets may be different. So {a, b, c} and {c, b, a} are called equal sets.
Equivalent
When two things cannot be compared directly, it is better not to call them equal. There is another word labeled equivalent that echoes this sentiment. Taking forward the example of sets given above, the sets are said to be equivalent if they have the same number of elements, but the elements are different. Thus, the sets {a, b, c} and {1, 2, 3} are said to be equivalent and not equal.
One cannot directly compare cats with dogs, but it is said that they are equivalent when it comes to making great companions for human beings. When two things are same in some specific way, they can be called equivalents. In geometry, a circle can be equivalent to a square if they have same areas, but they cannot be treated as equal. In chemistry, the concept of equivalence is used to categorize elements that have the same capacity to react or combine with other elements.
If there is a financial product that has been discontinued but still in demand, an insurance company comes up with a similar product that is said to be equivalent to the earlier product.
What is the difference between Equal and Equivalent?
• When two things have the same amount or quantity that can be measured as identical, the two things are said to be equal such as the weights or heights of two people, the color of two shirts or the size of two TV sets.
• When two things are same in some specific way, but not identical, they are said to be equivalent. Two triangles having same areas are said to be equivalent but not equal if other parameters are not the same.
• Two food items are said to be equivalent if they have the same health benefits for us.
• If your defective TV under warranty is replaced by vendor by another set, you have received an equivalent TV.