Why is 1 infinity undefined?

Infinity is a concept, not a number; therefore, the expression 1/infinity is actually undefined. In mathematics, a limit of a function occurs when x gets larger and larger as it approaches infinity, and 1/x gets smaller and smaller as it approaches zero.

Is 1 infinity defined?

It is used to represent an unimaginably big number, but you obviously can't tell which. Therefore, infinity itself is not a defined number.

Is 1 0 infinity or undefined?

But the limit of some expressions may take such forms when the variable takes a certain value and these are called indeterminate. Thus 1/0 is not infinity and 0/0 is not indeterminate, since division by zero is not defined.

Is an infinity limit undefined?

Since infinity is not a finite value, the limit of the function as x approaches 1 is undefined.

Is infinity +1 possible?

Yet even this relatively modest version of infinity has many bizarre properties, including being so vast that it remains the same, no matter how big a number is added to it (including another infinity). So infinity plus one is still infinity.

1^inf explained #IndeterminateFamily

Is Omega bigger than infinity?

ABSOLUTE INFINITY !!! This is the smallest ordinal number after "omega". Informally we can think of this as infinity plus one.

What is the value of 1 infinity?

Infinity is a concept, not a number; therefore, the expression 1/infinity is actually undefined.

What makes a limit undefined?

Sal gives an example of a limit where direct substitution ends in a quotient with 0 in the denominator and non-0 in the numerator. Such limits are undefined.

Is 1 undefined undefined?

To elaborate, neither 1 nor undefined are strings, so they're coerced to numbers. Number(undefined) is NaN , and 1 + NaN is still NaN .

Is infinity not defined?

First of all, infinity is not a real number so actually dividing something by zero is undefined. In calculus ∞ is an informal notion of something "larger than any finite number", but it's not a well-defined number.

Why is zero not defined?

The reason that the result of a division by zero is undefined is the fact that any attempt at a definition leads to a contradiction. a=r*b. r*0=a. (1) But r*0=0 for all numbers r, and so unless a=0 there is no solution of equation (1).

Is infinity a real number?

Infinity is a "real" and useful concept. However, infinity is not a member of the mathematically defined set of "real numbers" and, therefore, it is not a number on the real number line.

Why is 1 infinity an indeterminate form?

While at first this problem may not look like a 1 to infinity problem, it actually is because when you try to take a limit, you get 1 to infinity. Because you're dealing with limits, this 1 to infinity is an indeterminate form, as we discussed a moment ago, meaning it's an answer that you can't use.

Why do numbers never end?

The sequence of natural numbers never ends, and is infinite. OK, ¹/₃ is a finite number (it is not infinite). There's no reason why the 3s should ever stop: they repeat infinitely. So, when we see a number like "0.999..." (i.e. a decimal number with an infinite series of 9s), there is no end to the number of 9s.

Why is infinity not a number?

As far as describing it in an intelligent way, just say that infinity is not a number because infinity is a meta word not in the set but used to describe the set. Just as the words "unbounded" and "non-empty" are (usually) not considered as numbers, infinity is (often) not considered as a number.

Is infinity infinity indeterminate?

A limit confirmed to be infinity is not indeterminate since it has been determined to have a specific value (infinity).

Why is 0 infinity not indeterminate?

It claims that 0∞ is an indeterminate form because 0+∞ has the limiting value 0, and 0−∞ is equivalent to 1/0, which, as talked about in the same place I linked, is "not commonly regarded as an indeterminate form because there is not an infinite range of values that f/g could approach."

Why is infinity times 0 indeterminate?

Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication. In particular, infinity is the same thing as "1 over 0", so "zero times infinity" is the same thing as "zero over zero", which is an indeterminate form.

Why is infinity divided by infinity undefined?

Infinity is a concept for never-ending. Infinity + 1 is still infinity because there is an infinite amount of numbers out there and adding 1 to infinity will still result in the concept of infinity as well.

What is zero divided infinity?

Regardless of what large number we're dividing by our answer is 0 and by letting this large number increase (as much as we please, tending to infinity) the answer is still 0.

Is .9 repeating the same as 1?

This is what we mean when we say that 0.999... = 1 — the sequence of terminating decimals 0.9, 0.99, 0.999, 0.9999, and so on, converges to 1, so the repeating decimal 0.9999... representing the limit of that sequence, is said to be equal to 1.

Do numbers ever stop counting?

Whether you start counting backwards or forwards, numbers never seem to end.

Is G-O-O-G-L-E higher than infinity?

It's way bigger than a measly googol! Googolplex may well designate the largest number named with a single word, but of course that doesn't make it the biggest number. In a last-ditch effort to hold onto the hope that there is indeed such a thing as the largest number… Child: Infinity!

How long would it take to write out a googolplex?

Writing the number would take an immense amount of time: if a person can write two digits per second, then writing a googolplex would take about 1.51×10⁹² years, which is about 1.1×10⁸² times the accepted age of the universe.