-----BEGIN PRIVACY-ENHANCED MESSAGE-----
Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
Originator-Key-Asymmetric:
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 TWSM7vrzLADbmYQaionwg5sDW3P6oaM5D3tdezXMm7z1T+B+twIDAQAB
MIC-Info: RSA-MD5,RSA,
 OID4oAYTfS33WGqU6pt+aN/FiyXurpECyhatKhVpEbhrEizhoI7YvtcgfiEyXVFx
 2yLB3QyZFMST5lfRAyEvmA==

<SEC-DOCUMENT>0001209191-05-027483.txt : 20050520
<SEC-HEADER>0001209191-05-027483.hdr.sgml : 20050520
<ACCEPTANCE-DATETIME>20050520183451
ACCESSION NUMBER:		0001209191-05-027483
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20050520
FILED AS OF DATE:		20050520
DATE AS OF CHANGE:		20050520

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			INFINITY INC
		CENTRAL INDEX KEY:			0000822746
		STANDARD INDUSTRIAL CLASSIFICATION:	OIL, GAS FIELD SERVICES, NBC [1389]
		IRS NUMBER:				841070066
		STATE OF INCORPORATION:			CO
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		950 SEVENTEENTH STREET, SUITE 800
		CITY:			DENVER
		STATE:			CO
		ZIP:			80202
		BUSINESS PHONE:		720-932-7800

	MAIL ADDRESS:	
		STREET 1:		950 SEVENTEENTH STREET, SUITE 800
		CITY:			DENVER
		STATE:			CO
		ZIP:			80202

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Kaplan Elliot M
		CENTRAL INDEX KEY:			0001296603

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	000-17204
		FILM NUMBER:		05849417

	BUSINESS ADDRESS:	
		BUSINESS PHONE:		(816)221-3000

	MAIL ADDRESS:	
		STREET 1:		2405 GRAND BLVD., SUITE 900
		CITY:			KANSAS CITY
		STATE:			MO
		ZIP:			64108
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>bdn24125_bdn14emk.xml
<DESCRIPTION>MAIN DOCUMENT DESCRIPTION
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-05-20</periodOfReport>

    <issuer>
        <issuerCik>0000822746</issuerCik>
        <issuerName>INFINITY INC</issuerName>
        <issuerTradingSymbol>IFNY</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001296603</rptOwnerCik>
            <rptOwnerName>Kaplan Elliot M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2405 GRAND BLVD.</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 900</rptOwnerStreet2>
            <rptOwnerCity>KANSAS CITY</rptOwnerCity>
            <rptOwnerState>MO</rptOwnerState>
            <rptOwnerZipCode>64108</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2005-05-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1100</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>7.60</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4100</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <ownerSignature>
        <signatureName>James A. Tuell, as attorney-in-fact</signatureName>
        <signatureDate>2005-05-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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