The long tales of a tail/less ape

October 09, 2017 Monday

Bedtime Story

Free and Bound Variables

To understand the concept of combinatory logic, we need to understand the idea of free and bound variables.

It is well known by all of you that the most common variable used in mathematics is x.

Since it can have any value depending upon the equation or the function, it is otherwise a free variable.

Let me show you how a free variable such as x can become a bound variable.

When I spell out an equation that says there exists x such as x² = 4, then that free variable x becomes a bound variable.

It now has a definite identity attached to it.

Another example where you can bind down the free variable x is as follows:

‘For all x, (x+1)² = x² + 2x + 1’

Here again x will be limited by the solution to this quadratic equation.

So far we have considered only a single variable x.

Now let us consider some expressions that have multiple variables and then study the concept of free and bound.

Consider the following expressions

∑ f (k, n) where k = 1 to 10

In the above expression, n is a free variable and k is a bound variable.

This is so because the eventual value of this expression would depend on n whereas k can have only value from 1 to 10.

It is a variable but has been bounded between 1 and 10.

Now let us consider this integration expression.

∫0 to infinity x ↑ (y-1) e↑(-x) dx

In this expression y is a free variable and x is a bound variable.

This is so because y has not been assigned any value but x on the other hand has been assigned values from zero to infinity.

You may argue that the values that x has been assigned is infinite, yet the fact remains that it has been assigned some value whereas y has not.

With this much, you have a fairly modest understanding of the notion of free and bound variables with respect to mathematical expressions.

What works for pure mathematical expressions also holds true for mathematical logic.

In mathematical logic too there exist such free and bound variables.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.com

Good night mon ami and my fellow cousin ape.

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Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

All his books can be downloaded for free through this link:

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

Monday, October 9, 2017