Množice števil so temelj vse matematike, ki jo boš uporabljal... Show more
Matematika
Angleščina
GeografijaSign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
117
•
Updated Apr 15, 2026
•
Vrste števil in njihove značilnosti
1 / 6
Uvod v množice števil
Predstavljaj si množice števil kot različne škatle, kjer v vsako spadajo števila z določenimi lastnostmi. Naravna števila (N) so tista, s katerimi šteješ - 1, 2, 3, 4... Torej N = {1, 2, 3, 4, ...}.
Cela števila (Z) dodajo negativna števila in ničlo. Tako dobiš Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}. Vsako naravno število je tudi celo število, zato velja N ⊂ Z.
Racionalna števila (Q) so tista, ki jih lahko zapišeš kot ulomek dveh celih števil (imenovalec ni 0). Vključujejo cela števila, ulomke, končna decimalna števila in periodična decimalna števila.
💡 Pomni: Ime "racionalna" prihaja iz latinske besede "ratio" (razmerje), ker gre za razmerje med dvema celima številoma!
Racionalna in iracionalna števila
Racionalna števila prepoznaš po tem, da imajo končen ali periodičen decimalni zapis. Primeri: 0,25 = 1/4, 0,333... = 1/3, ali 5 = 5/1.
Iracionalna števila (I) so ravno nasprotje - ne moreš jih zapisati kot ulomek. Njihov decimalni zapis je neskončen in neperiodičen (števke se nikoli ne začnejo ponavljati v vzorcu).
Najznamenitejši primeri iracionalnih števil so π ≈ 3,14159..., √2, √3, √5. Pozor - √9 ni iracionalno, ker je √9 = 3!
💡 Test za korene: Če je število pod korenom popoln kvadrat, rezultat ni iracionalen. √16 = 4 (racionalno), √17 (iracionalno).
Realna števila in povezanost množic
Realna števila (R) so največja množica, ki jo poznamo - vključujejo vsa racionalna in iracionalna števila. Vsako realno število ima svoje mesto na številski premici.
Povezanost med množicami si predstavljaj kot matruške: N ⊂ Z ⊂ Q ⊂ R. Vsaka manjša množica je vsebovana v večji. Iracionalna števila (I) so ločena od racionalnih, vendar skupaj tvorita realna števila: R = Q ∪ I.
Ključna razlika za prepoznavanje: racionalna števila imajo končen ali periodičen decimalni zapis, iracionalna pa neskončen in neperiodičen.
💡 Za test: Zapomni si odnos N ⊂ Z ⊂ Q ⊂ R in to, da sta Q in I ločeni množici brez skupnih elementov.
Praktični primeri razvrščanja
Poglejmo, kako razvrščamo števila v množice na konkretnih primerih:
-7: Ni naravno, je celo (Z), racionalno (Q), ker -7 = -7/1, in realno (R). 21/7: Najprej poenostavi: 21/7 = 3. Spada v N, Z, Q, R. 5,1: Ni naravno ali celo, je racionalno (5,1 = 51/10) in realno.
√11: 11 ni popoln kvadrat, zato je √11 iracionalno in realno število. 0,272727...: To je periodično decimalno število, zato je racionalno in realno.
Pri korenih vedno preveri, ali je število pod korenom popoln kvadrat. √64 = 8 je racionalno, √65 pa iracionalno.
💡 Trik: Pri decimalnih številih pazi na vzorec - če se števke ponavljajo, je število racionalno!
Pomembni nasveti za test
Ključne razlike za prepoznavanje: Racionalna števila lahko zapišeš kot ulomek ali imajo končen/periodičen decimalni zapis. Iracionalna imajo neskončen, neperiodičen decimalni zapis.
Oznake si zapomni: N (naravna), Z , Q , I (iracionalna), R (realna).
Pogosti primeri: π, e, √2, √3, √5 so iracionalna. Vsi ulomki, cela števila in periodična decimalna števila so racionalna.
Vsako število, s katerim se srečuješ v 1. letniku, je realno število. Če ti naloga ne pove drugače, lahko predpostavljaš, da delamo z realnimi števili.
💡 Za ponavljanje: N ⊂ Z ⊂ Q ⊂ R, Q ∩ I = ∅ (nimata skupnih elementov), R = Q ∪ I.
Povzetek po množicah
| Množica | Simbol | Kaj vključuje | Primeri |
|---|---|---|---|
| **Naravna** | N | Števila za štetje | 1, 5, 120 |
| **Cela** | Z | Naravna + nič + negativna | -10, 0, 4 |
| **Racionalna** | Q | Lahko zapišeš kot ulomek | 3, -0,5, 7, 0,6̄ |
| **Iracionalna** | I | Neskončen neperiodičen zapis | √2, π, e |
| **Realna** | R | Vsa števila na premici | Vsi zgornji |
Ta preglednica ti bo pomagala pri hitrem ponavljanju pred testom. Zapomni si glavno logiko: manjše množice so vedno del večjih, razen iracionalne, ki je ločena od racionalne.
💡 Zadnji nasvet: Če se ti zdi število "običajno", je verjetno racionalno. Če vsebuje π, e ali koren nepopolnega kvadrata, je iracionalno!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Matematika
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Vrste števil in njihove značilnosti
Množice števil so temelj vse matematike, ki jo boš uporabljal v srednji šoli in naprej. Gre za organizacijo vseh števil v logične skupine, kjer vsaka ima svoja posebna pravila in lastnosti.
Uvod v množice števil
Predstavljaj si množice števil kot različne škatle, kjer v vsako spadajo števila z določenimi lastnostmi. Naravna števila (N) so tista, s katerimi šteješ - 1, 2, 3, 4... Torej N = {1, 2, 3, 4, ...}.
Cela števila (Z) dodajo negativna števila in ničlo. Tako dobiš Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}. Vsako naravno število je tudi celo število, zato velja N ⊂ Z.
Racionalna števila (Q) so tista, ki jih lahko zapišeš kot ulomek dveh celih števil (imenovalec ni 0). Vključujejo cela števila, ulomke, končna decimalna števila in periodična decimalna števila.
💡 Pomni: Ime "racionalna" prihaja iz latinske besede "ratio" (razmerje), ker gre za razmerje med dvema celima številoma!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Racionalna in iracionalna števila
Racionalna števila prepoznaš po tem, da imajo končen ali periodičen decimalni zapis. Primeri: 0,25 = 1/4, 0,333... = 1/3, ali 5 = 5/1.
Iracionalna števila (I) so ravno nasprotje - ne moreš jih zapisati kot ulomek. Njihov decimalni zapis je neskončen in neperiodičen (števke se nikoli ne začnejo ponavljati v vzorcu).
Najznamenitejši primeri iracionalnih števil so π ≈ 3,14159..., √2, √3, √5. Pozor - √9 ni iracionalno, ker je √9 = 3!
💡 Test za korene: Če je število pod korenom popoln kvadrat, rezultat ni iracionalen. √16 = 4 (racionalno), √17 (iracionalno).
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Realna števila in povezanost množic
Realna števila (R) so največja množica, ki jo poznamo - vključujejo vsa racionalna in iracionalna števila. Vsako realno število ima svoje mesto na številski premici.
Povezanost med množicami si predstavljaj kot matruške: N ⊂ Z ⊂ Q ⊂ R. Vsaka manjša množica je vsebovana v večji. Iracionalna števila (I) so ločena od racionalnih, vendar skupaj tvorita realna števila: R = Q ∪ I.
Ključna razlika za prepoznavanje: racionalna števila imajo končen ali periodičen decimalni zapis, iracionalna pa neskončen in neperiodičen.
💡 Za test: Zapomni si odnos N ⊂ Z ⊂ Q ⊂ R in to, da sta Q in I ločeni množici brez skupnih elementov.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Praktični primeri razvrščanja
Poglejmo, kako razvrščamo števila v množice na konkretnih primerih:
-7: Ni naravno, je celo (Z), racionalno (Q), ker -7 = -7/1, in realno (R). 21/7: Najprej poenostavi: 21/7 = 3. Spada v N, Z, Q, R. 5,1: Ni naravno ali celo, je racionalno (5,1 = 51/10) in realno.
√11: 11 ni popoln kvadrat, zato je √11 iracionalno in realno število. 0,272727...: To je periodično decimalno število, zato je racionalno in realno.
Pri korenih vedno preveri, ali je število pod korenom popoln kvadrat. √64 = 8 je racionalno, √65 pa iracionalno.
💡 Trik: Pri decimalnih številih pazi na vzorec - če se števke ponavljajo, je število racionalno!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Pomembni nasveti za test
Ključne razlike za prepoznavanje: Racionalna števila lahko zapišeš kot ulomek ali imajo končen/periodičen decimalni zapis. Iracionalna imajo neskončen, neperiodičen decimalni zapis.
Oznake si zapomni: N (naravna), Z , Q , I (iracionalna), R (realna).
Pogosti primeri: π, e, √2, √3, √5 so iracionalna. Vsi ulomki, cela števila in periodična decimalna števila so racionalna.
Vsako število, s katerim se srečuješ v 1. letniku, je realno število. Če ti naloga ne pove drugače, lahko predpostavljaš, da delamo z realnimi števili.
💡 Za ponavljanje: N ⊂ Z ⊂ Q ⊂ R, Q ∩ I = ∅ (nimata skupnih elementov), R = Q ∪ I.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Povzetek po množicah
| Množica | Simbol | Kaj vključuje | Primeri |
|---|---|---|---|
| **Naravna** | N | Števila za štetje | 1, 5, 120 |
| **Cela** | Z | Naravna + nič + negativna | -10, 0, 4 |
| **Racionalna** | Q | Lahko zapišeš kot ulomek | 3, -0,5, 7, 0,6̄ |
| **Iracionalna** | I | Neskončen neperiodičen zapis | √2, π, e |
| **Realna** | R | Vsa števila na premici | Vsi zgornji |
Ta preglednica ti bo pomagala pri hitrem ponavljanju pred testom. Zapomni si glavno logiko: manjše množice so vedno del večjih, razen iracionalne, ki je ločena od racionalne.
💡 Zadnji nasvet: Če se ti zdi število "običajno", je verjetno racionalno. Če vsebuje π, e ali koren nepopolnega kvadrata, je iracionalno!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
1
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Practice Test ✓ Essay Outlines
Practice Test
Quiz
Flashcards
Essay
Most popular content in Matematika
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user