Positive Integers In The Interval [-2, 5]: Explained!

Hey guys! Let's dive into a fun math problem today! We're going to figure out how many positive integers are chilling in the interval [-2, 5]. Don't worry, it's not as scary as it sounds! We'll break it down step by step so it's super easy to understand.

Understanding the Question

Okay, so the question is: How many positive integers are there in the interval [-2, 5], considering the set of positive natural numbers N* = {1, 2, 3, 4, 5, ...}? Let's dissect this thing! First off, what are positive integers? Simply put, these are whole numbers greater than zero (1, 2, 3, and so on). We're not talking about fractions, decimals, or negative numbers here, just good ol' whole numbers. Now, what's an interval? In math terms, an interval is a set of numbers between two given endpoints. In our case, the interval is [-2, 5]. The square brackets mean we include the endpoints, so -2 and 5 are part of the party. However, since we are looking for positive integers, we can ignore the negative numbers and zero.

To really nail this, let’s talk about the notation N*. This represents the set of positive natural numbers, which are the same as positive integers. They start at 1 and go on forever (1, 2, 3, 4, 5, ...). Knowing this definition is key because it tells us exactly which numbers we should be counting within our interval. So, armed with this knowledge, we're ready to tackle the problem head-on and find out how many positive integers fit the bill. It's all about understanding the terms and taking it one step at a time, making math a whole lot less intimidating!

Identifying Positive Integers within the Range

Now let's get down to the nitty-gritty of identifying the positive integers within the range [-2, 5]. Remember, we're only interested in whole numbers greater than zero. So, let’s consider our interval [-2, 5]. This means we're looking at all the numbers from -2 up to 5, including -2 and 5 themselves. But hold on! We're only after positive integers, which changes the game a bit. We can immediately ditch any negative numbers and zero from our consideration, because they don't fit the criteria. That means -2, -1, and 0 are out.

So, what's left? Let's start from the positive side. We have 1, 2, 3, 4, and 5. All of these numbers are positive and whole, meaning they fit perfectly into our definition of positive integers. They also fall within our interval of [-2, 5]. It's like finding the right pieces of a puzzle! To make it super clear, let’s list them out: 1, 2, 3, 4, 5. These are the only positive integers that reside within the interval [-2, 5]. We’ve successfully narrowed down our options by understanding what the question is asking for and applying the definitions of intervals and positive integers. Next, we’ll count them up and find our answer. See? We're making progress, and it's all about taking those steps carefully!

Counting the Positive Integers

Alright, we've done the hard part – identifying the positive integers! Now comes the super easy part: counting them. We've already established that the positive integers within the interval [-2, 5] are 1, 2, 3, 4, and 5. So, how many numbers are in that list? Let's count them one by one: 1, 2, 3, 4, 5. That's a total of five numbers! So, we have five positive integers nestled within our specified range. Isn't that satisfying when everything clicks into place?

This step is crucial because it directly answers the question. We've gone from understanding the problem to figuring out which numbers qualify, and now we're simply counting those numbers. It highlights the importance of breaking down a problem into smaller, manageable steps. By first understanding the definition of positive integers and the meaning of the interval, we were able to easily pinpoint the relevant numbers. Then, counting them was a breeze! This methodical approach can be applied to all sorts of math problems, making them less daunting and more, dare I say, fun! Now that we've counted our positive integers, we're ready to select the correct answer from the options provided. Let's move on to that final step!

Selecting the Correct Answer

Okay, we've cracked the code! We know there are five positive integers in the interval [-2, 5]. Now, let's match that up with the answer choices. The question usually gives you some options to pick from, and this is where we confirm our hard work. So, let's imagine we have these choices:

A) 2 B) 3 C) 4 D) 5

Which one matches our answer? You guessed it – D) 5! We found five positive integers, and option D confirms that. It's always a good feeling when your calculations align perfectly with the choices given. This step is super important because it’s where we make sure we're answering the specific question asked. We’re not just doing math for the fun of it (though that's cool too!), we’re aiming to select the correct answer.

This process also highlights the importance of accuracy in each step. If we misidentified the positive integers or miscounted them, we might end up choosing the wrong answer. But because we took our time and followed a logical process, we arrived at the correct solution. So, when you're tackling math problems, always double-check your work and make sure your final answer makes sense in the context of the question. Now, let's wrap things up with a quick recap to solidify our understanding!

Conclusion

Alright guys, let’s wrap this up and give ourselves a pat on the back! We successfully tackled the question of how many positive integers are in the interval [-2, 5]. We started by understanding the question, making sure we knew what positive integers were and what the interval meant. Then, we identified the positive integers within the range, which were 1, 2, 3, 4, and 5. After that, we simply counted them, finding a total of five positive integers. And finally, we selected the correct answer from the choices provided, which was D) 5.

This whole process shows how breaking down a problem into smaller steps can make it much easier to solve. We didn't just jump to an answer; we took a methodical approach, ensuring we understood each part along the way. Remember, math isn’t about speed; it’s about accuracy and understanding. So, the next time you face a similar problem, take a deep breath, break it down, and follow the steps. You’ve got this! And who knows, maybe you'll even start enjoying math a little more along the way. Keep practicing, keep learning, and most importantly, keep having fun with it! 😃